Worked Example • Hot Dog & Bun Pair

LCM of 8 and 10 (Equals 40)

The Least Common Multiple of 8 and 10 is 40. Both numbers are even with GCF(8, 10) = 2, so dividing their product (80) by 2 gives LCM(8, 10) = 40.

LCM of 8 and 10 Result

LCM(8, 10) = 40

Greatest Common Factor: GCF(8, 10) = 2

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

40 ÷ 8 = 540 ÷ 10 = 4

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.

8 = 2 × 2 × 2

= 2³

10 = 2 × 5

= 2 × 5

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

Prime	In 8	In 10	Highest Power
2	2³	2¹	2³ = 8
5	—	5¹	5¹ = 5

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

LCM = 2³ × 5¹ = 8 × 5 = 40

Full Written Solution for the LCM of 8 and 10

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(8, 10) = 40:

Method A: Prime Factorization

• 8 = 2³
• 10 = 2 × 5

Multiply the highest power of each prime: 2³ × 5¹ = 40.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 8 and 10 is 2.

40 ÷ 8 = 5 (remainder 0 ✓)

40 ÷ 10 = 4 (remainder 0 ✓)

Real-World & Fraction Context

Classic grocery problem: hot dogs come in packs of 8 and buns come in bags of 10. Buying 5 packs of hot dogs and 4 bags of buns gives 40 of each with zero waste.

Mistake to Watch Out For

Writing 8 × 10 = 80 is twice as large as needed because both 8 and 10 are divisible by 2.