Worked Example • Origin of the 60-Minute Hour

LCM of 10 and 12 (Equals 60)

The Least Common Multiple of 10 and 12 is 60. Both numbers are even with GCF(10, 12) = 2, so LCM(10, 12) = (10 × 12) ÷ 2 = 60.

LCM of 10 and 12 Result

LCM(10, 12) = 60

Greatest Common Factor: GCF(10, 12) = 2

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

60 ÷ 10 = 660 ÷ 12 = 5

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.

10 = 2 × 5

= 2 × 5

12 = 2 × 2 × 3

= 2² × 3

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

Prime	In 10	In 12	Highest Power
2	2¹	2²	2² = 4
3	—	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(10, 12) = 60:

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

The Greatest Common Factor of 10 and 12 is 2.

60 ÷ 10 = 6 (remainder 0 ✓)

60 ÷ 12 = 5 (remainder 0 ✓)

Two buses departing every 10 minutes and every 12 minutes will pull out of the terminal together every 60 minutes (once every hour on the dot).

Since every multiple of 10 ends in zero, just walk up the 12-times table until you hit a zero in the ones place: 12, 24, 36, 48, 60.