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Least Common Multiple of 6 and 9

Least common multiple (LCM) of 6 and 9 is 18.

LCM(6,9) = 18

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

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Least Common Multiple of 6 and 9 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 9, than apply into the LCM equation.

GCF(6,9) = 3
LCM(6,9) = ( 6 × 9) / 3
LCM(6,9) = 54 / 3
LCM(6,9) = 18

Least Common Multiple (LCM) of 6 and 9 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 9. First we will calculate the prime factors of 6 and 9.

Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 21 × 31

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 32

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 9.

LCM(6,9) = 21 × 32
LCM(6,9) = 18

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