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Least Common Multiple (LCM)

Definition of Least Common Multiple

• Least common multiple is the smallest nonzero number that is a common multiple of two or more numbers considered.

Examples of Least Common Multiple

• The LCM of 6, 9, 15 is 90.

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, . . .

9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, .

15: 15, 30, 45, 60, 75, 90, . . .

• Finding LCM comes handy while adding, subtracting, or comparing two or more fractions with unlike denominators.
• Least Common Denominator: Least common denominator is the least common multiple of the denominators of the fractions with unlike denominators.

### Solved Example on Least Common Multiple

Find the least common multiple of 13 and 11.

Choices:

A. 13

B. 24

C. 143

D. 11

Solution:

Step 1: As 13 and 11 are coprimes, the least common multiple is nothing but their product.

Step 2: So, least common multiple of 13 and 11 is 143.

Related Terms for Least Common Multiple

• Multiple
• Common Multiple