Worked Example • Multiples of 5

LCM of 15 and 20 (Equals 60)

The Least Common Multiple of 15 and 20 is 60. Since 15 (3 × 5) and 20 (2² × 5) share a Greatest Common Factor of 5, their LCM is (15 × 20) ÷ 5 = 60.

LCM of 15 and 20 Result

LCM(15, 20) = 60

Greatest Common Factor: GCF(15, 20) = 5

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

60 ÷ 15 = 460 ÷ 20 = 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.

15 = 3 × 5

= 3 × 5

20 = 2 × 2 × 5

= 2² × 5

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

Prime	In 15	In 20	Highest Power
2	—	2²	2² = 4
3	3¹	—	3¹ = 3
5	5¹	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(15, 20) = 60:

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

The Greatest Common Factor of 15 and 20 is 5.

60 ÷ 15 = 4 (remainder 0 ✓)

60 ÷ 20 = 3 (remainder 0 ✓)

Tiling a square patio area with 15 cm × 20 cm rectangular pavers creates a smallest square module of 60 cm × 60 cm (4 rows by 3 columns).

Don't stop at 30 (30 is not divisible by 20) and don't multiply 15 × 20 = 300.