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What is the Least Common Multiple of 12108 and 12120?

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 12108 and 12120 is 12229080.

LCM(12108,12120) = 12229080

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Least Common Multiple of 12108 and 12120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12108 and 12120, than apply into the LCM equation.

GCF(12108,12120) = 12
LCM(12108,12120) = ( 12108 × 12120) / 12
LCM(12108,12120) = 146748960 / 12
LCM(12108,12120) = 12229080

Least Common Multiple (LCM) of 12108 and 12120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12108 and 12120. First we will calculate the prime factors of 12108 and 12120.

Prime Factorization of 12108

Prime factors of 12108 are 2, 3, 1009. Prime factorization of 12108 in exponential form is:

12108 = 22 × 31 × 10091

Prime Factorization of 12120

Prime factors of 12120 are 2, 3, 5, 101. Prime factorization of 12120 in exponential form is:

12120 = 23 × 31 × 51 × 1011

Now multiplying the highest exponent prime factors to calculate the LCM of 12108 and 12120.

LCM(12108,12120) = 23 × 31 × 10091 × 51 × 1011
LCM(12108,12120) = 12229080