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What is the Least Common Multiple of 9 and 12?

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.

Least common multiple (LCM) of 9 and 12 is 36.

LCM(9,12) = 36

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Least Common Multiple of 9 and 12 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 12, than apply into the LCM equation.

GCF(9,12) = 3
LCM(9,12) = ( 9 × 12) / 3
LCM(9,12) = 108 / 3
LCM(9,12) = 36

Least Common Multiple (LCM) of 9 and 12 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 12. First we will calculate the prime factors of 9 and 12.

Prime Factorization of 9

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

9 = 32

Prime Factorization of 12

Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:

12 = 22 × 31

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 12.

LCM(9,12) = 32 × 22
LCM(9,12) = 36

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