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Worked Example • Twin Odd Primes

LCM of 3 and 5 (Equals 15)

The Least Common Multiple of 3 and 5 is 15. Both 3 and 5 are distinct prime numbers, which guarantees their Greatest Common Factor is 1 and their LCM is 3 × 5 = 15.

2 to 10 integers • up to 18 digits each
Parsed:35
LCM of 3 and 5 Result
LCM(3, 5) = 15
Greatest Common Factor: GCF(3, 5) = 1No common factor greater than 1
Check the answer (every division leaves a remainder of 0):
15 ÷ 3 = 515 ÷ 5 = 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.

3 = 3
= 3(prime)
5 = 5
= 5(prime)

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

PrimeIn 3In 5Highest Power
33¹—3¹ = 3
5—5¹5¹ = 5

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

LCM = 3¹ × 5¹ = 3 × 5 = 15

Full Written Solution for the LCM of 3 and 5

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(3, 5) = 15:

Method A: Prime Factorization

  • • 3 = 3
  • • 5 = 5

Multiply the highest power of each prime: 3¹ × 5¹ = 15.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 3 and 5 is 1.

15 ÷ 3 = 5 (remainder 0 ✓)
15 ÷ 5 = 3 (remainder 0 ✓)

Real-World & Fraction Context

If one lighthouse flashes every 3 seconds and a second buoy flashes every 5 seconds, both beacons will flash at the exact same instant every 15 seconds (four times per minute).

Mistake to Watch Out For

Watch out when checking 30: while 30 ends in 0 and is divisible by both 3 and 5, you passed the odd match at 15 halfway there.