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Worked Example • Classic Textbook Intro Pair

LCM of 4 and 6 (Equals 12)

The Least Common Multiple of 4 and 6 is 12 (not 24). Because 4 and 6 are both even numbers that share a Greatest Common Factor of 2, dividing their product (4 × 6 = 24) by 2 gives the true LCM of 12.

2 to 10 integers • up to 18 digits each
Parsed:46
LCM of 4 and 6 Result
LCM(4, 6) = 12
Greatest Common Factor: GCF(4, 6) = 2
Check the answer (every division leaves a remainder of 0):
12 ÷ 4 = 312 ÷ 6 = 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.

4 = 2 × 2
= 2²
6 = 2 × 3
= 2 × 3

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

PrimeIn 4In 6Highest Power
22²2¹2² = 4
3—3¹3¹ = 3

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

LCM = 2² × 3¹ = 4 × 3 = 12

Full Written Solution for the LCM of 4 and 6

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(4, 6) = 12:

Method A: Prime Factorization

  • • 4 = 2²
  • • 6 = 2 × 3

Multiply the highest power of each prime: 2² × 3¹ = 12.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 4 and 6 is 2.

12 ÷ 4 = 3 (remainder 0 ✓)
12 ÷ 6 = 2 (remainder 0 ✓)

Real-World & Fraction Context

If you are adding 1/4 + 1/6 on a worksheet, using 12 as your Least Common Denominator gives 3/12 + 2/12 = 5/12 in one step, without needing to reduce 10/24 at the end.

Mistake to Watch Out For

Writing 4 × 6 = 24 is the #1 mistake on 5th-grade fraction quizzes. Always check if both numbers are even; if they are, their LCM is at most half of their product.