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Fraction Operations Lessons

Least Common Multiple: Learn

The Least Common Multiple (LCM) is the smallest number that two or more numbers will divide into evenly.

For a single number it is easy to find multiples by simply multiplying the number by increasing whole numbers (or, more simply "counting by" that number).

Example: multiples of 4 are 4, 8, 12, 16, 20, 24, and so on.

There are two good ways to find the Least Common Multiple of two numbers. Here's the first way:

  • Find the Greatest Common Factor (GCF) of the numbers
  • Multiply the numbers together
  • Divide the product of the numbers by the GCF.

An an example of this method, consider the numbers 15 and 12. Their GCF is 3, so the LCM is 15*12÷3 = 180÷3 = 60.

Alternatively, you could begin counting by the larger number until you reach a multiple which is also a multiple of the smaller number.

For example, again consider 15 and 12. Fifteen is the larger number, so start counting by fifteens:
15 - no, not a multiple of 12
30 - no, not a multiple of 12
45 - no, not a multiple of 12
60 - yes, 12*5=60 so 60 is the LCM.

LCM: Practice

What is the LCM of the two numbers?

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The LCM of and is:

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