Worked Example • Consecutive Pair

LCM of 5 and 6 (Equals 30)

The Least Common Multiple of 5 and 6 is 30. Because 5 and 6 are consecutive whole numbers, they share no common factors greater than 1 (GCF = 1), so LCM(5, 6) = 5 × 6 = 30.

LCM of 5 and 6 Result

LCM(5, 6) = 30

Greatest Common Factor: GCF(5, 6) = 1No common factor greater than 1

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

30 ÷ 5 = 630 ÷ 6 = 5

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.

5 = 5

= 5(prime)

6 = 2 × 3

= 2 × 3

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

Prime	In 5	In 6	Highest Power
2	—	2¹	2¹ = 2
3	—	3¹	3¹ = 3
5	5¹	—	5¹ = 5

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

LCM = 2¹ × 3¹ × 5¹ = 2 × 3 × 5 = 30

Full Written Solution for the LCM of 5 and 6

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(5, 6) = 30:

Method A: Prime Factorization

• 5 = 5
• 6 = 2 × 3

Multiply the highest power of each prime: 2¹ × 3¹ × 5¹ = 30.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 5 and 6 is 1.

30 ÷ 5 = 6 (remainder 0 ✓)

30 ÷ 6 = 5 (remainder 0 ✓)

Real-World & Fraction Context

In a 30-day month like April or June, tasks scheduled every 5 days and every 6 days both fall together on Day 30.

Mistake to Watch Out For

Because 5 is prime and 6 = 2 × 3, their prime factor lists have zero overlap. This is one of the cases where multiplying straight across is 100% right.