Worked Example • Prime & Cube of 2

LCM of 7 and 8 (Equals 56)

The Least Common Multiple of 7 and 8 is 56. Because 7 is prime and 8 (2³) is consecutive to 7, they share no common factors (GCF = 1), so LCM(7, 8) = 7 × 8 = 56.

LCM of 7 and 8 Result

LCM(7, 8) = 56

Greatest Common Factor: GCF(7, 8) = 1No common factor greater than 1

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

56 ÷ 7 = 856 ÷ 8 = 7

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.

7 = 7

= 7(prime)

8 = 2 × 2 × 2

= 2³

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

Prime	In 7	In 8	Highest Power
2	—	2³	2³ = 8
7	7¹	—	7¹ = 7

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

LCM = 2³ × 7¹ = 8 × 7 = 56

Full Written Solution for the LCM of 7 and 8

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(7, 8) = 56:

Method A: Prime Factorization

• 7 = 7
• 8 = 2³

Multiply the highest power of each prime: 2³ × 7¹ = 56.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 7 and 8 is 1.

56 ÷ 7 = 8 (remainder 0 ✓)

56 ÷ 8 = 7 (remainder 0 ✓)

Real-World & Fraction Context

If a weekly backup runs every 7 days and an 8-day rotation shift starts on the same Monday, both land on the same day again after 56 days (exactly 8 weeks).

Mistake to Watch Out For

7 × 8 = 56 is one of the trickiest single-digit multiplication facts to recall under time pressure—remember the sequential digits '5, 6, 7, 8' (56 = 7 × 8).