Worked Example • Large Shared Factor (GCF = 12)

LCM of 24 and 36 (Equals 72)

The Least Common Multiple of 24 and 36 is 72. Because 24 and 36 both sit in the 12-times table with GCF(24, 36) = 12, their LCM is (24 ÷ 12) × 36 = 2 × 36 = 72.

LCM of 24 and 36 Result

LCM(24, 36) = 72

Greatest Common Factor: GCF(24, 36) = 12

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

72 ÷ 24 = 372 ÷ 36 = 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.

24 = 2 × 2 × 2 × 3

= 2³ × 3

36 = 2 × 2 × 3 × 3

= 2² × 3²

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

Prime	In 24	In 36	Highest Power
2	2³	2²	2³ = 8
3	3¹	3²	3² = 9

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

LCM = 2³ × 3² = 8 × 9 = 72

Full Written Solution for the LCM of 24 and 36

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(24, 36) = 72:

Method A: Prime Factorization

• 24 = 2³ × 3
• 36 = 2² × 3²

Multiply the highest power of each prime: 2³ × 3² = 72.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 24 and 36 is 12.

72 ÷ 24 = 3 (remainder 0 ✓)

72 ÷ 36 = 2 (remainder 0 ✓)

Real-World & Fraction Context

Two photography strobes or industrial conveyors on 24-second and 36-second cycles fire together every 72 seconds.

Mistake to Watch Out For

If you only divide out 6 instead of the full GCF of 12, you will get 144 instead of 72.