How to find the Lowest Common Multiple (LCM) #6

00:05:42
https://www.youtube.com/watch?v=RMJs_I9Nydw

摘要

TLDRThe video explains the process of finding the least common multiple (LCM) of a set of numbers. The LCM is the smallest number that is a multiple of all given numbers. One method is listing the multiples of each number and picking the smallest common one, like when finding the LCM of 6 and 10, which is 30. Another method involves using prime factors to simplify the process, especially with larger numbers, to avoid lengthy lists. For example, the LCM of 28 and 42 using their prime factors is 84. Key advice includes practicing examples to become more familiar with the concept.

心得

  • 🔢 The LCM is the smallest number that is a multiple of all numbers in the set.
  • 📝 Listing multiples helps find the LCM for smaller numbers.
  • 🤔 Multiplying the original numbers gives a common multiple but not necessarily the LCM.
  • 🔍 Prime factorization simplifies finding the LCM for larger numbers.
  • 👍 Practice makes understanding LCM easier.
  • ✅ The LCM of 6 and 10 is 30.
  • ✅ The LCM of 5 and 8 is 40.
  • ✅ Using prime factors, the LCM of 28 and 42 is 84.
  • 💡 Prime factors should only be counted once if they appear in both lists.
  • ✅ The LCM of 132 and 420 using prime factors is 4620.

时间轴

  • 00:00:00 - 00:05:42

    This video explains how to find the least common multiple (LCM) of a set of numbers by listing their multiples and choosing the smallest common one. An example with numbers 6 and 10 shows 30 as the LCM. It warns against using the multiplication shortcut, which doesn't always give the LCM, and demonstrates finding the LCM for numbers 5 and 8 using the listing method, resulting in 40 as the LCM. It also introduces a shortcut using prime factors for finding the LCM of larger numbers, using the example of 28 and 42, resulting in an LCM of 84. The process involves multiplying all prime factors, ensuring shared primes are only counted once. Finally, it applies the prime factor method to 132 and 420 to find their LCM, 4620, and encourages practice to master the technique.

思维导图

Mind Map

常见问题

  • How do you find the least common multiple (LCM)?

    List the multiples of each number and pick the smallest number that occurs in all of the lists.

  • What is the lowest common multiple of 6 and 10?

    The lowest common multiple of 6 and 10 is 30.

  • Can you find LCM by multiplying the numbers together?

    Multiplying the numbers together will give a common multiple, but not necessarily the least common multiple.

  • What is the lowest common multiple of 5 and 8?

    The lowest common multiple of 5 and 8 is 40.

  • What is the significance of prime factors in finding the LCM?

    Prime factors can be used to find the LCM by multiplying all unique prime factors from both lists.

  • How to find the LCM of 28 and 42 using prime factors?

    Multiply the unique prime factors of both numbers, 2, 3, and 7, to get 84 as the LCM.

  • What is the easiest method to find LCM for larger numbers?

    Using prime factors of each number simplifies finding the LCM, especially for larger numbers.

  • What should you do if you're confused about finding LCM?

    Practice questions to get used to the concept, as it may seem confusing initially.

  • What is the lowest common multiple of 132 and 420?

    The lowest common multiple of 132 and 420 is 4620.

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  • 00:00:04
    in this video we're going to cover how
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    you find the least common multiple
  • 00:00:09
    which we can also call the lowest common
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    multiple or lcm
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    the lowest common multiple of a set of
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    numbers is the smallest number that is a
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    multiple of all the numbers in the
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    question
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    so to find it we can just list the
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    multiples of each number and pick the
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    smallest number that occurs in all of
  • 00:00:32
    the lists
  • 00:00:35
    for example if we wanted to find the
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    lowest common multiple of 6 and 10
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    we'd write out the first few multiples
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    of 6
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    or hs6 12 18 24 30 and 36
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    and then do the same thing for 10
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    so 10
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    20 30 40 50.
  • 00:00:59
    then we'd look at both of these lists
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    and find the first number that occurs in
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    both of them
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    which is 30.
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    if we had carried on going though
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    we'd have seen that 60 also occurs in
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    both of the lists
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    so 60 is also a common multiple
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    however because 30 is a lower number
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    30 is the lowest common multiple
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    which is what we're trying to find
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    this point is actually really important
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    because one of the shortcuts that some
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    students take
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    is to multiply together the numbers that
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    we're looking at
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    so in this case they have multiplied
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    together 6 and 10
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    to get 60.
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    this technique will always give you a
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    common multiple
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    but it won't always be the least common
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    multiple
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    which means that sometimes you won't get
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    the correct answer
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    so it's much better to use the technique
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    that we just used and list out all of
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    the multiples
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    have a go at doing the same thing for
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    this question
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    so here we've been asked to find the
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    least common multiple of five and eight
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    so the first thing we need to do is list
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    out the multiples of each
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    which are 5 10 15 20 and so on four five
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    and then 8 16 24 32 and so on for eight
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    then if we compare these two lists
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    we can see that 40 is the only multiple
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    that's common to both lists
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    and therefore 40 must be the lowest
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    common multiple or lcm
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    now sometimes this technique can end up
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    taking ages particularly if the numbers
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    involved are quite big
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    if we have the prime factors of each
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    number though then there is an easier
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    way to do it
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    for example in this question we're being
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    asked to find the lowest common multiple
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    of 28 and 42
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    and we're given the prime factors of
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    each one in the question
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    to find the lowest common multiple we
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    have to look at prime factors of each
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    one
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    and multiply together all the prime
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    factors of both numbers
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    but importantly if a number occurs in
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    both lists we only count it once
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    so because there are two of these twos
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    here
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    we'd only count one of them and we can
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    cross the other one out
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    whereas would include both this two
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    and this three
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    and then because the sevens occur in
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    both lists we again only include one of
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    them so we can cross one of them out
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    and so overall we end up doing two times
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    two times three times seven
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    to get 84
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    which would be our lowest common
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    multiple
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    and if you want to check this
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    we could have a look at these two lists
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    which are the multiples of 28 and 42
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    and you can see that 84 is the one that
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    occurs in both
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    so it is the lowest common multiple
  • 00:04:23
    one thing i want to say here is don't
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    worry if you're finding this a bit
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    confusing at first
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    it is a kind of odd concept
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    and the best thing to do is just to
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    practice a few questions and after a
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    while you'll get used to it
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    let's try one more before we finish
  • 00:04:42
    so this time we're trying to find the
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    lowest common multiple of 132 and 420
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    just like before we need to look at the
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    prime factors of each
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    and cross out all the ones that are the
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    same in both lists
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    so we can cross out this two
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    this two
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    and this three
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    then we multiply together all of these
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    numbers that we have left
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    so two times two times three times five
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    times seven times eleven
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    which would give us four thousand six
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    hundred and twenty as our lowest common
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    multiple
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    and that's everything for this video
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    so cheers for watching
  • 00:05:31
    and we'll see you again soon
  • 00:05:42
    you
标签
  • least common multiple
  • LCM
  • multiples
  • prime factors
  • common multiple
  • math tutorial