Applying LCM in Problems

Let’s list the multiples: 6, 12, 18, 24… and 8, 16, 24… The first number that appears in both lists is 24. That’s the least common multiple.

Multiples of 9 are 9, 18, 27, 36, 45… and for 15: 15, 30, 45… They meet at 45. So 45 is the smallest number both divide evenly into.

Twelve’s multiples: 12, 24, 36, 48, 60… Twenty’s multiples: 20, 40, 60… The first common multiple is 60.

Both share the factor 7 (14 = 2×7, 21 = 3×7). Multiply 7 by 2 and 3 to get 7×2×3 = 42.

The highest powers of prime factors are 2³ and 3². Multiply 8×9 = 72. That’s the LCM.

25 = 5² and 30 = 2×3×5. Include each factor’s highest power: 2×3×5² = 150.

Multiples of 8: 8, 16, 24, 32, 40… and 10: 10, 20, 30, 40… They meet at 40.

They share no factors, so multiply 4×9 = 36.

Common factors are 2 and 5; combine everything (2²×3×5) = 60.

Both have 5 as a factor, and 15 = 3×5, 25 = 5². Multiply 3×5² = 75.

27 = 3³, 18 = 2×3². Use 2×3³ = 54.

Each contains 7. Combine 2²×3×7 = 84.

16 = 2⁴, 20 = 2²×5. Use 2⁴×5 = 80.

2³ and 3² → 2³×3² = 72.

Factors 2²×3×5 = 60.

No common factors, so 5×18 = 90.

All primes 2, 3, 5, 7 → 2×3×5×7 = 210.

They’re both prime, so 11×13 = 143.

No common factors, multiply 19×20 = 380.

Common factor 11. So 2×3×11 = 66.