﻿ least common multiple | mathtestpreparation.com
back to per-algebra

# Least Common Multiple

Least Common Multiple (LCM)
The amallest number that is a multiple of two or more whole numbers is the least common multiple of the number.
Example 1:
Find the least common multiple (LCM) of 6, 8, and 16.
Solution:
Multiple of 6: 6, 12, 18, 24, 30, 36, 42, 48,...
Multiple of 8: 8, 16, 24, 32, 40, 48,...
Multiple of 16: 16, 32, 48,...
Since 6 × 8 = 48, 8 × 6 = 48, 16 × 3 = 48
Therefore, the least common multiple (LCM) of 6, 8, and 16 is 48.
Fing the least common multiple (LCM) of 20 and 24 by using prime factoring. 20 = 2 × 2 × 5. 24 = 2 × 2 × 2 × 3.
Both numbers have common factors 2 × 2.
20 has an extra factor 5.
24 has extra factors 2 × 3.
The least common multiple (LCM) of 20 and 24 is: 2 × 2 × 5 × 2 × 3 = 120.

The least common multiple (LCM) of two or more numbers is the multiplication of the common factors and the extra factors of these numbers.

The least common multiple (LCM) is used to find the least common denominator LCD when perform the addtion and subtraction of two or more fractions.