GCF and LCM of 30 and 45
The greatest common factor and least common multiple of 30 and 45.
GCF of 30 and 45
15
LCM of 30 and 45
90
How it works
Break each number into its prime factors:
- 30 = 2 × 3 × 5
- 45 = 3² × 5
The GCF (15) multiplies the primes both share, at the lowest power each appears. The LCM (90) multiplies every prime that appears in either number, at the highest power — which is also 30 × 45 ÷ 15 = 90.
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Frequently asked questions
What is the GCF of 30 and 45?+
The greatest common factor (GCF) of 30 and 45 is 15 — the largest number that divides both 30 and 45 with no remainder.
What is the LCM of 30 and 45?+
The least common multiple (LCM) of 30 and 45 is 90 — the smallest number that both 30 and 45 divide into. It equals 30 × 45 ÷ GCF = 1350 ÷ 15 = 90.