Worked Example • Percentage Benchmark (100)

LCM of 20 and 25 (Equals 100)

The Least Common Multiple of 20 and 25 is 100. Both numbers are divisible by 5 (GCF = 5), so LCM(20, 25) = (20 × 25) ÷ 5 = 100.

LCM of 20 and 25 Result

LCM(20, 25) = 100

Greatest Common Factor: GCF(20, 25) = 5

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

100 ÷ 20 = 5100 ÷ 25 = 4

Show the Working (Step-by-Step)

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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.

20 = 2 × 2 × 5

= 2² × 5

25 = 5 × 5

= 5²

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

Prime	In 20	In 25	Highest Power
2	2²	—	2² = 4
5	5¹	5²	5² = 25

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

LCM = 2² × 5² = 4 × 25 = 100

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(20, 25) = 100:

Multiply the highest power of each prime: 2² × 5² = 100.

The Greatest Common Factor of 20 and 25 is 5.

100 ÷ 20 = 5 (remainder 0 ✓)

100 ÷ 25 = 4 (remainder 0 ✓)

In US currency or metric coins, 20-cent pieces and 25-cent quarters reach their first equal dollar amount at 100 cents ($1.00).

Multiplying 20 × 25 = 500 forgets to divide out their shared factor of 5.