Worked Example • Clock-Face Benchmark

LCM of 12 and 15 (Equals 60)

The Least Common Multiple of 12 and 15 is 60. Because 12 (2² × 3) and 15 (3 × 5) share a common factor of 3, their LCM is (12 × 15) ÷ 3 = 60.

LCM of 12 and 15 Result

LCM(12, 15) = 60

Greatest Common Factor: GCF(12, 15) = 3

Check the answer (every division leaves a remainder of 0):

60 ÷ 12 = 560 ÷ 15 = 4

Show the Working (Step-by-Step)

Switch method in one click:

Step 1: Break each number down into its prime factors.

Write each input as a product of prime numbers, then group matching primes with exponents.

12 = 2 × 2 × 3

= 2² × 3

15 = 3 × 5

= 3 × 5

Step 2: For each prime, pick the highest exponent that appears in any single number.

Prime	In 12	In 15	Highest Power
2	2²	—	2² = 4
3	3¹	3¹	3¹ = 3
5	—	5¹	5¹ = 5

Step 3: Multiply those highest prime powers together to get the LCM.

LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(12, 15) = 60:

Multiply the highest power of each prime: 2² × 3¹ × 5¹ = 60.

The Greatest Common Factor of 12 and 15 is 3.

60 ÷ 12 = 5 (remainder 0 ✓)

60 ÷ 15 = 4 (remainder 0 ✓)

When adding 5/12 + 4/15, LCD(12, 15) = 60 converts the problem into 25/60 + 16/60 = 41/60.

12 × 15 = 180 is three times too big because both 12 and 15 are divisible by 3.