LCM and GCD

Greatest Common Divisor (GCD)

The GCD (also called HCF) is the biggest number that divides two numbers exactly.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6. GCD = 6.

Least Common Multiple (LCM)

The LCM is the smallest number that both numbers divide into exactly.

Multiples of 4: 4, 8, 12, 16, 20, 24

Multiples of 6: 6, 12, 18, 24

LCM = 12.

Using prime factors

12 = 2 x 2 x 3; 18 = 2 x 3 x 3

• GCD: multiply the common primes: 2 x 3 = 6
• LCM: multiply all primes using the highest powers: 2 x 2 x 3 x 3 = 36

Word problem

Two bells ring every 4 minutes and 6 minutes. If they ring together at 8:00 a.m., when will they next ring together? LCM of 4 and 6 = 12, so at 8:12 a.m.