Worked Example • Shared Factor of 5

LCM of 10 and 15 (Equals 30)

The Least Common Multiple of 10 and 15 is 30. Because both numbers end in 0 or 5, they share a Greatest Common Factor of 5, giving LCM(10, 15) = (10 × 15) ÷ 5 = 30.

LCM of 10 and 15 Result

LCM(10, 15) = 30

Greatest Common Factor: GCF(10, 15) = 5

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

30 ÷ 10 = 330 ÷ 15 = 2

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

15 = 3 × 5

= 3 × 5

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

Prime	In 10	In 15	Highest Power
2	2¹	—	2¹ = 2
3	—	3¹	3¹ = 3
5	5¹	5¹	5¹ = 5

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

LCM = 2¹ × 3¹ × 5¹ = 2 × 3 × 5 = 30

Full Written Solution for the LCM of 10 and 15

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(10, 15) = 30:

Method A: Prime Factorization

• 10 = 2 × 5
• 15 = 3 × 5

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

Method B: GCF & Exact Division Check

The Greatest Common Factor of 10 and 15 is 5.

30 ÷ 10 = 3 (remainder 0 ✓)

30 ÷ 15 = 2 (remainder 0 ✓)

Real-World & Fraction Context

In a half-hour (30-minute) TV block, 10-minute segments (3 per show) and 15-minute segments (2 per show) align cleanly at the 30-minute mark.

Mistake to Watch Out For

Multiplying 10 × 15 = 150 forgets that both numbers sit in the 5-times table.