The LCM of 84 and 204 is:

Concept

The least common multiple of positive integers is the smallest positive number divisible by each integer.

Using prime factorization, take every prime that occurs and retain its highest exponent across the numbers.

Application

1. Factor 84: 84 = 22 × 3 × 7.

2. Factor 204: 204 = 22 × 3 × 17.

3. Select the highest required powers: 22, 3, 7, and 17.

4. Multiply them: 22 × 3 × 7 × 17 = 4 × 3 × 119 = 1428.

Cross-check

1. 1428 ÷ 84 = 17, an integer.

2. 1428 ÷ 204 = 7, an integer.

Therefore, the LCM of 84 and 204 is 1428.