Worked Example • Direct Multiple

LCM of 5 and 10 (Equals 10)

The Least Common Multiple of 5 and 10 is 10. Since 10 is already a multiple of 5 (5 × 2 = 10), 10 is the smallest positive integer divisible by both 5 and 10.

LCM of 5 and 10 Result

LCM(5, 10) = 10

Greatest Common Factor: GCF(5, 10) = 5

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

10 ÷ 5 = 210 ÷ 10 = 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.

5 = 5

= 5(prime)

10 = 2 × 5

= 2 × 5

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

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

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

LCM = 2¹ × 5¹ = 2 × 5 = 10

Full Written Solution for the LCM of 5 and 10

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(5, 10) = 10:

Method A: Prime Factorization

• 5 = 5
• 10 = 2 × 5

Multiply the highest power of each prime: 2¹ × 5¹ = 10.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 5 and 10 is 5.

10 ÷ 5 = 2 (remainder 0 ✓)

10 ÷ 10 = 1 (remainder 0 ✓)

Real-World & Fraction Context

Converting 3/5 to tenths so you can add it to 1/10 uses LCD(5, 10) = 10: 3/5 becomes 6/10, and 6/10 + 1/10 = 7/10.

Mistake to Watch Out For

Students moving too fast on a worksheet often write 5 × 10 = 50, or write 5 because they confused LCM with GCF.