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What is the Least Common Multiple of 6120 and 6132?

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 6120 and 6132 is 3127320.

LCM(6120,6132) = 3127320

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Least Common Multiple of 6120 and 6132 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6120 and 6132, than apply into the LCM equation.

GCF(6120,6132) = 12
LCM(6120,6132) = ( 6120 × 6132) / 12
LCM(6120,6132) = 37527840 / 12
LCM(6120,6132) = 3127320

Least Common Multiple (LCM) of 6120 and 6132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6120 and 6132. First we will calculate the prime factors of 6120 and 6132.

Prime Factorization of 6120

Prime factors of 6120 are 2, 3, 5, 17. Prime factorization of 6120 in exponential form is:

6120 = 23 × 32 × 51 × 171

Prime Factorization of 6132

Prime factors of 6132 are 2, 3, 7, 73. Prime factorization of 6132 in exponential form is:

6132 = 22 × 31 × 71 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 6120 and 6132.

LCM(6120,6132) = 23 × 32 × 51 × 171 × 71 × 731
LCM(6120,6132) = 3127320