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Least common multiple review

Review least common multiples (LCM) and try some practice problems.

What is LCM?

LCM stands for least common multiple. The least common multiple of two numbers is the smallest number that is a multiple of both of them.

Finding least common multiple

One way to find the LCM of two (or more!) numbers is to list the multiples of each number until we find the smallest multiple they have in common.
Want to learn more about least common multiples? Check out this video.

Example 1: LCM of 8 and 10

Multiples of 8: 8, comma, 16, comma, 24, comma, 32, comma, start color #11accd, 40, end color #11accd, comma, 48, comma, 56, comma, 64, comma, 72, comma, start color #11accd, 80, end color #11accd, point, point, point
Multiples of 10: 10, comma, 20, comma, 30, comma, start color #11accd, 40, end color #11accd, comma, 50, comma, 60, comma, 70, comma, start color #11accd, 80, end color #11accd, comma, 90, comma, 100, point, point, point
start color #11accd, 40, end color #11accd and start color #11accd, 80, end color #11accd are common multiples of 8 and 10. Which of these is the least?
start color #11accd, 40, end color #11accd is the smallest multiple that 8 and 10 have in common.
start text, l, c, m, end text, left parenthesis, 8, comma, 10, right parenthesis, equals, 40

Example 2: LCM of 3, comma, 4, comma and 6

Multiples of 3: 3, comma, 6, comma, 9, comma, start color #11accd, 12, end color #11accd, comma, 15, comma, 18, comma, 21, comma, start color #11accd, 24, end color #11accd, point, point, point
Multiples of 4: 4, comma, 8, comma, start color #11accd, 12, end color #11accd, comma, 16, comma, 20, comma, start color #11accd, 24, end color #11accd, comma, 28, point, point, point
Multiples of 6: 6, comma, start color #11accd, 12, end color #11accd, comma, 18, comma, start color #11accd, 24, end color #11accd, comma, 30, comma, 36, point, point, point
start color #11accd, 12, end color #11accd is the smallest multiple that 3, comma, 4, comma and 6 have in common.
start text, l, c, m, end text, left parenthesis, 3, comma, 4, comma, 6, right parenthesis, equals, 12

Practice

Problem 1
  • Current
What is the least common multiple of 3 and 9?
Another way to say this is:
start text, l, c, m, end text, left parenthesis, 3, comma, 9, right parenthesis, equals, question mark
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

  • duskpin seedling style avatar for user simrahquazi42
    I think the easiest way is to write down the multiples and then find it.
    (54 votes)
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  • duskpin seed style avatar for user Cristela Bonilla
    This is very easy for me but others who dont get it should watch the video and take down the notes because that is how it helped me. For sure theyre gonna get it next time!
    (33 votes)
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  • blobby green style avatar for user 2023bbailey
    I get it i'm just need a little more work that's all.
    (30 votes)
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  • duskpin sapling style avatar for user hgnairne11
    When i finished the whole thing for l.c.m i played: i feel good and danced!
    (22 votes)
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  • duskpin seedling style avatar for user Trixie23
    how one question make some more question please.
    (17 votes)
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  • blobby green style avatar for user meleenah153
    so this is kinda hard idk how to actually figure it out without looking it up....
    (12 votes)
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  • blobby green style avatar for user aaron richards
    what is the LCM of 8,10,and 23
    (9 votes)
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  • cacteye blue style avatar for user 27eembleton
    i did not have to watch the video but the people that may have to here is a little tip......... it is just skip counting intill the 2 or more numbers you have finaly have the same number the first one you find will be the least
    (7 votes)
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  • blobby green style avatar for user madigdingus
    Is there another way to find the gcf?
    (6 votes)
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  • piceratops tree style avatar for user Aarnev ( :
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    (4 votes)
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