GCF of 12 and 18
The greatest common factor of 12 and 18 is 6. Their least common multiple is 36.
- Answer with working
- LCM included
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Why the GCF of 12 and 18 is 6
- Break each number into primes: 12 = 2² × 3 and 18 = 2 × 3².
- Keep only the primes in both lists, each at its lower power: 2 × 3.
- Multiply those together: the GCF is 6.
The factors 12 and 18 share are 1, 2, 3, 6. The largest of them is 6, which is another way of getting the same answer.
For the least common multiple, take every prime at its higher power instead: the LCM of 12 and 18 is 36. A quick check: 12 × 18 = 216, and 216 ÷ 6 = 36.
Find the GCF
Whole numbers, separated by spaces, commas or new lines.
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How to find the greatest common factor
Factor each number
24 = 2³ × 3, 36 = 2² × 3², 60 = 2² × 3 × 5.
Keep the shared primes
Take each prime that appears in every number, at its lowest power: 2² and 3.
Multiply them
2² × 3 = 12. The GCF of 24, 36 and 60 is 12. For the LCM, take every prime at its highest power: 2³ × 3² × 5 = 360.
GCF is also called GCD (greatest common divisor) and HCF (highest common factor). Same thing.
Questions people ask
What is the GCF of 12 and 18?
6. It is the largest whole number that divides both 12 and 18 exactly.
What is the LCM of 12 and 18?
36. It is the smallest whole number that both 12 and 18 divide into.
What are the common factors of 12 and 18?
1, 2, 3, 6. The greatest of them, 6, is the GCF.
Is GCF the same as GCD and HCF?
Yes. Greatest common factor, greatest common divisor and highest common factor all mean the same thing.
What is the difference between GCF and LCM?
GCF is the biggest number that divides into all of them; LCM is the smallest number they all divide into. For 4 and 6, the GCF is 2 and the LCM is 12.
What is the GCF if one number is 0?
The GCF of 0 and any number n is n itself, because every number divides 0. The LCM with 0 is undefined.
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