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Worked Example • Mutually Coprime Triple

LCM of 3, 4, and 5 (Equals 60)

The Least Common Multiple of 3, 4, and 5 is 60. Because no two numbers in the list (3, 4, 5) share any prime factor, they are pairwise coprime, so LCM(3, 4, 5) = 3 × 4 × 5 = 60.

2 to 10 integers • up to 18 digits each
Parsed:345
LCM of 3, 4, and 5 Result
LCM(3, 4, 5) = 60
Greatest Common Factor: GCF(3, 4, 5) = 1No common factor greater than 1
Check the answer (every division leaves a remainder of 0):
60 ÷ 3 = 2060 ÷ 4 = 1560 ÷ 5 = 12

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.

3 = 3
= 3(prime)
4 = 2 × 2
= 2²
5 = 5
= 5(prime)

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

PrimeIn 3In 4In 5Highest Power
2—2²—2² = 4
33¹——3¹ = 3
5——5¹5¹ = 5

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

LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60

Full Written Solution for the LCM of 3, 4, and 5

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(3, 4, 5) = 60:

Method A: Prime Factorization

  • • 3 = 3
  • • 4 = 2²
  • • 5 = 5

Multiply the highest power of each prime: 2² × 3¹ × 5¹ = 60.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 3, 4, and 5 is 1.

60 ÷ 3 = 20 (remainder 0 ✓)
60 ÷ 4 = 15 (remainder 0 ✓)
60 ÷ 5 = 12 (remainder 0 ✓)

Real-World & Fraction Context

A teacher with 60 chairs in an auditorium can arrange them in equal rows of 3, equal rows of 4, or equal rows of 5 with zero chairs left over.

Mistake to Watch Out For

Always verify pairwise coprimality before multiplying three numbers: check (3,4), (4,5), and (3,5). Here all three pairs have GCF = 1.