Worked Example • Shared Factor of 8

LCM of 16 and 24 (Equals 48)

The Least Common Multiple of 16 and 24 is 48. Both numbers are multiples of 8 (GCF = 8), so LCM(16, 24) = (16 × 24) ÷ 8 = 48.

LCM of 16 and 24 Result

LCM(16, 24) = 48

Greatest Common Factor: GCF(16, 24) = 8

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

48 ÷ 16 = 348 ÷ 24 = 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.

16 = 2 × 2 × 2 × 2

= 2⁴

24 = 2 × 2 × 2 × 3

= 2³ × 3

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

Prime	In 16	In 24	Highest Power
2	2⁴	2³	2⁴ = 16
3	—	3¹	3¹ = 3

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

LCM = 2⁴ × 3¹ = 16 × 3 = 48

Full Written Solution for the LCM of 16 and 24

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(16, 24) = 48:

Method A: Prime Factorization

• 16 = 2⁴
• 24 = 2³ × 3

Multiply the highest power of each prime: 2⁴ × 3¹ = 48.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 16 and 24 is 8.

48 ÷ 16 = 3 (remainder 0 ✓)

48 ÷ 24 = 2 (remainder 0 ✓)

Real-World & Fraction Context

A 16-tooth gear driving a 24-tooth gear realigns its marked teeth every 48 tooth clicks (3 revolutions of the 16-tooth gear, 2 revolutions of the 24-tooth gear).

Mistake to Watch Out For

If you only divide out a common factor of 4 instead of the full GCF of 8, you get 96 instead of 48.