Worked Example • Odd Composites Sharing 3

LCM of 9 and 15 (Equals 45)

The Least Common Multiple of 9 and 15 is 45. Since 9 (3²) and 15 (3 × 5) share a Greatest Common Factor of 3, their LCM is (9 × 15) ÷ 3 = 45.

LCM of 9 and 15 Result

LCM(9, 15) = 45

Greatest Common Factor: GCF(9, 15) = 3

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

45 ÷ 9 = 545 ÷ 15 = 3

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.

9 = 3 × 3

= 3²

15 = 3 × 5

= 3 × 5

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

Prime	In 9	In 15	Highest Power
3	3²	3¹	3² = 9
5	—	5¹	5¹ = 5

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

LCM = 3² × 5¹ = 9 × 5 = 45

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(9, 15) = 45:

Multiply the highest power of each prime: 3² × 5¹ = 45.

The Greatest Common Factor of 9 and 15 is 3.

45 ÷ 9 = 5 (remainder 0 ✓)

45 ÷ 15 = 3 (remainder 0 ✓)

A 45-minute school period can be split into three 15-minute lab rotations or five 9-minute presentation slots.

Watch out for 9 × 15 = 135; dividing out the shared factor of 3 first ((9 ÷ 3) × 15 = 3 × 15 = 45) keeps the calculation tiny.