LCM (Least Common Multiple) LCM of two positive integers is the smallest number that both can divide into.
Method 1: Using Prime Factorization
Find LCM of 60 and 84
Step 1: Prime factorize both numbers
60 = 22 × 3 × 5
84 = 22 × 3 × 7
Step 2: Take all prime factors with the highest powers:
22 × 3 × 5
22 × 3 × 7
Prime factors with the highest powers: 22, 3, 5, 7
LCM = 22 × 3 × 5 × 7
LCM = 4 × 3 × 5 × 7
LCM = 420
Find LCM of 12 and 18
Step 1: Prime factorize both numbers
12 = 2² × 3
18 = 2 × 3²
Step2: Take all prime factors with the highest powers
2² × 3
2 × 3²
Prime factors with the highest powers: 2², 3²
LCM = 2² × 3²
LCM = 4 × 9
LCM = 36
Find LCM of 15 and 20
Step 1: Prime factorize both numbers
15 = 3 × 5
20 = 2² × 5
Step2: Take all prime factors with the highest powers
3 × 5
2² × 5
Prime factors with the highest powers: 2², 3, 5
LCM = 2² × 3 × 5
LCM = 4 × 3 × 5
LCM = 60
Find LCM of 8 and 14
Step 1: Prime factorize both numbers
8 = 2³
14 = 2 × 7
Step2: Take all prime factors with the highest powers
8 = 2³
14 = 2 × 7
Prime factors with the highest powers: 2³, 7
LCM = 2³ × 7
LCM = 8 × 7
LCM = 56
Method 2: Using the Euclidean Algorithm
The Euclidean Algorithm finds the GCD faster using repeated division.
LCM (a, b) = ab / GCD(a, b)
Find LCM of 60 and 84
Step 1: Find GCD using Euclidean Algorithm
84 ÷ 60 = 1 remainder 24
60 ÷ 24 = 2 remainder 12
24 ÷ 12 = 2 remainder 0
GCD (60, 84) = 12
Step 2: Solve LCM (a,b) = ab / GCD(a, b)
LCM (60,84) = ((60) (84)) / 12
LCM (60,84) = 5040 / 12
LCM (60,84) = 420
Find LCM of 12 and 18
Step 1: Find GCD using Euclidean Algorithm
18 ÷ 12 = 1 remainder 6
12 ÷ 6 = 2 remainder 0
GCD (12, 18) = 6
Step 2: Solve LCM (a,b) = ab / GCD(a, b)
LCM (12,18) = ((12) (18)) / 6
LCM (12,18) = 216 / 6
LCM (12,18) = 36
Find LCM of 15 and 20
Step 1: Find GCD using Euclidean Algorithm
20 ÷ 15 = 1 remainder 5
15 ÷ 5 = 3 remainder 0
GCD (15, 20) = 5
Step 2: Solve LCM (a,b) = ab / GCD(a, b)
LCM (15,20) = ((15) (20)) / 5
LCM (12,18) = 300 / 5
LCM (12,18) = 60