Worked Examples

Example A — Two numbers: LCM(15, 20)

1. GCD(15, 20): 20 = 1×15 + 5; 15 = 3×5 + 0 → GCD = 5
2. LCM = 15 × 20 ÷ 5 = 60
3. Check by primes: 15 = 3×5, 20 = 2²Ã—5 → 2²Ã—3×5 = 60 ✓

Example B — Three numbers: LCM(12, 18, 24)

1. LCM(12, 18) = 12×18 / GCD(12,18) = 216 / 6 = 36
2. LCM(36, 24) = 36×24 / GCD(36,24) = 864 / 12 = 72

Example C — Coprime pair: LCM(7, 11)

GCD(7,11)=1, so LCM = 7×11 = 77. Whenever two numbers share no prime factors, the LCM is just their product.

Example D — Adding fractions

Compute 1/8 + 5/12.

1. LCM(8,12) = 24
2. 1/8 = 3/24, 5/12 = 10/24
3. Sum = 13/24

Example E — Schedule problem

Lamp A blinks every 6 seconds, lamp B every 10, lamp C every 15. When do they blink together?

LCM(6,10,15): LCM(6,10)=30; LCM(30,15)=30. They sync every 30 seconds.