Understanding Least Common Multiple (LCM)

What is a Least Common Multiple?

A multiple is the result of multiplying a number by an integer. The Least Common Multiple (LCM) of two numbers is the smallest positive number that is a multiple of both.

For instance, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.

How to Find the LCM

Listing Multiples:

• Multiples of 4: 4, 8, 12, 16, 20, 24
• Multiples of 6: 6, 12, 18, 24 The smallest matching number is 12.

Using the GCF Formula: There's a beautiful relationship between GCF and LCM: LCM(a, b) = (a × b) / GCF(a, b)

Using our 4 and 6 example:

• The GCF of 4 and 6 is 2.
• 4 × 6 = 24
• 24 / 2 = 12

This formula is highly efficient, especially when dealing with large numbers.