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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.

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