Worked Example • Dozen vs. Pound Ounces

LCM of 12 and 16 (Equals 48)

The Least Common Multiple of 12 and 16 is 48. Both numbers are divisible by 4 (GCF = 4), so LCM(12, 16) = (12 × 16) ÷ 4 = 48.

LCM of 12 and 16 Result

LCM(12, 16) = 48

Greatest Common Factor: GCF(12, 16) = 4

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

48 ÷ 12 = 448 ÷ 16 = 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.

12 = 2 × 2 × 3

= 2² × 3

16 = 2 × 2 × 2 × 2

= 2⁴

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

Prime	In 12	In 16	Highest Power
2	2²	2⁴	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 12 and 16

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(12, 16) = 48:

Method A: Prime Factorization

• 12 = 2² × 3
• 16 = 2⁴

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

Method B: GCF & Exact Division Check

The Greatest Common Factor of 12 and 16 is 4.

48 ÷ 12 = 4 (remainder 0 ✓)

48 ÷ 16 = 3 (remainder 0 ✓)

Real-World & Fraction Context

In Imperial measurements (12 inches per foot, 16 ounces per pound) or 1/12 and 1/16 architectural scale drawings, 48 is the smallest grid unit that divides cleanly into both.

Mistake to Watch Out For

Dividing by 2 instead of the full GCF of 4 gives 96 instead of 48.