Least Common Multiple Math Example 2

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Example 2

medium

Find the LCM of

8

12

, and

15

Solution

1
Prime factorizations: $8 = 2^3$ , $12 = 2^2 \times 3$ , $15 = 3 \times 5$ .
2
Take the maximum exponent of each prime: $2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5$ .
3
Compute: $8 \times 3 = 24$ , then $24 \times 5 = 120$ .

Answer

120

For multiple numbers, find all primes that appear in any factorization and take the highest power of each. The LCM is essential for adding fractions with different denominators.

About Least Common Multiple

The smallest positive integer that is divisible by each of two or more given numbers—where their multiples first coincide.

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More Least Common Multiple Examples

Example 1 easy

Find the LCM of [formula] and [formula].

Example 3 easy

Find the LCM of [formula] and [formula].

Example 4 easy

Two lights flash every [formula] seconds and every [formula] seconds. If they flash together now, af

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Related Concepts

Multiples Adding Fractions