Worked Example • Even Composite Pair

LCM of 6 and 10 (Equals 30)

The Least Common Multiple of 6 and 10 is 30. Both numbers are even with a shared factor of 2, so LCM(6, 10) = (6 × 10) ÷ 2 = 30.

LCM of 6 and 10 Result

LCM(6, 10) = 30

Greatest Common Factor: GCF(6, 10) = 2

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

30 ÷ 6 = 530 ÷ 10 = 3

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.

6 = 2 × 3

= 2 × 3

10 = 2 × 5

= 2 × 5

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

Prime	In 6	In 10	Highest Power
2	2¹	2¹	2¹ = 2
3	3¹	—	3¹ = 3
5	—	5¹	5¹ = 5

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

LCM = 2¹ × 3¹ × 5¹ = 2 × 3 × 5 = 30

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(6, 10) = 30:

Multiply the highest power of each prime: 2¹ × 3¹ × 5¹ = 30.

The Greatest Common Factor of 6 and 10 is 2.

30 ÷ 6 = 5 (remainder 0 ✓)

30 ÷ 10 = 3 (remainder 0 ✓)

Two assembly machines that cycle every 6 seconds and 10 seconds complete a synchronized cycle every 30 seconds (twice per minute).

Multiplying 6 × 10 = 60 forgets to divide out GCF(6, 10) = 2.