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What is the Least Common Multiple of 7149 and 7164?

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 7149 and 7164 is 17071812.

LCM(7149,7164) = 17071812

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Least Common Multiple of 7149 and 7164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7149 and 7164, than apply into the LCM equation.

GCF(7149,7164) = 3
LCM(7149,7164) = ( 7149 × 7164) / 3
LCM(7149,7164) = 51215436 / 3
LCM(7149,7164) = 17071812

Least Common Multiple (LCM) of 7149 and 7164 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7149 and 7164. First we will calculate the prime factors of 7149 and 7164.

Prime Factorization of 7149

Prime factors of 7149 are 3, 2383. Prime factorization of 7149 in exponential form is:

7149 = 31 × 23831

Prime Factorization of 7164

Prime factors of 7164 are 2, 3, 199. Prime factorization of 7164 in exponential form is:

7164 = 22 × 32 × 1991

Now multiplying the highest exponent prime factors to calculate the LCM of 7149 and 7164.

LCM(7149,7164) = 32 × 23831 × 22 × 1991
LCM(7149,7164) = 17071812