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Worked Example • Direct Divisibility Rule

LCM of 4 and 8 (Equals 8)

The Least Common Multiple of 4 and 8 is 8. Because 4 divides evenly into 8 (8 ÷ 4 = 2), 8 is already a multiple of 4, making the larger number (8) the LCM automatically.

2 to 10 integers • up to 18 digits each
Parsed:48
LCM of 4 and 8 Result
LCM(4, 8) = 8
Greatest Common Factor: GCF(4, 8) = 4
Check the answer (every division leaves a remainder of 0):
8 ÷ 4 = 28 ÷ 8 = 1

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
8 = 2 × 2 × 2
= 2³

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

PrimeIn 4In 8Highest Power
22²2³2³ = 8

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

LCM = 2³ = 8

Full Written Solution for the LCM of 4 and 8

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(4, 8) = 8:

Method A: Prime Factorization

  • • 4 = 2²
  • • 8 = 2³

Multiply the highest power of each prime: 2³ = 8.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 4 and 8 is 4.

8 ÷ 4 = 2 (remainder 0 ✓)
8 ÷ 8 = 1 (remainder 0 ✓)

Real-World & Fraction Context

When measuring carpentry cuts in 1/4-inch and 3/8-inch increments, you convert quarters directly into eighths (2/8 + 3/8 = 5/8 inch) because LCD(4, 8) = 8.

Mistake to Watch Out For

Do not multiply 4 × 8 = 32, and do not answer 4 (4 is the Greatest Common Factor of 4 and 8, whereas 8 is the Least Common Multiple).