Worked Example • Shared Factor of 2

LCM of 4 and 10 (Equals 20)

The Least Common Multiple of 4 and 10 is 20. Both numbers are even with GCF(4, 10) = 2, so their LCM is half of their product: (4 × 10) ÷ 2 = 20.

LCM of 4 and 10 Result

LCM(4, 10) = 20

Greatest Common Factor: GCF(4, 10) = 2

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

20 ÷ 4 = 520 ÷ 10 = 2

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.

4 = 2 × 2

= 2²

10 = 2 × 5

= 2 × 5

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

Prime	In 4	In 10	Highest Power
2	2²	2¹	2² = 4
5	—	5¹	5¹ = 5

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

LCM = 2² × 5¹ = 4 × 5 = 20

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(4, 10) = 20:

Multiply the highest power of each prime: 2² × 5¹ = 20.

The Greatest Common Factor of 4 and 10 is 2.

20 ÷ 4 = 5 (remainder 0 ✓)

20 ÷ 10 = 2 (remainder 0 ✓)

If one garden sprinkler rotates every 4 seconds and another every 10 seconds, they will spray in sync every 20 seconds.

Multiplying 4 × 10 = 40 overlooks that both 4 and 10 are even. Halving 40 gives the smallest common multiple, 20.