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What is the Least Common Multiple of 9 and 15?

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 15 is 45.

LCM(9,15) = 45

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Least Common Multiple of 9 and 15 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 15, than apply into the LCM equation.

GCF(9,15) = 3
LCM(9,15) = ( 9 × 15) / 3
LCM(9,15) = 135 / 3
LCM(9,15) = 45

Least Common Multiple (LCM) of 9 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 15. First we will calculate the prime factors of 9 and 15.

Prime Factorization of 9

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

9 = 32

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

15 = 31 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 15.

LCM(9,15) = 32 × 51
LCM(9,15) = 45

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