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What is the Least Common Multiple of 48096 and 48102?

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 48096 and 48102 is 385585632.

LCM(48096,48102) = 385585632

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Least Common Multiple of 48096 and 48102 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48096 and 48102, than apply into the LCM equation.

GCF(48096,48102) = 6
LCM(48096,48102) = ( 48096 × 48102) / 6
LCM(48096,48102) = 2313513792 / 6
LCM(48096,48102) = 385585632

Least Common Multiple (LCM) of 48096 and 48102 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48096 and 48102. First we will calculate the prime factors of 48096 and 48102.

Prime Factorization of 48096

Prime factors of 48096 are 2, 3, 167. Prime factorization of 48096 in exponential form is:

48096 = 25 × 32 × 1671

Prime Factorization of 48102

Prime factors of 48102 are 2, 3, 8017. Prime factorization of 48102 in exponential form is:

48102 = 21 × 31 × 80171

Now multiplying the highest exponent prime factors to calculate the LCM of 48096 and 48102.

LCM(48096,48102) = 25 × 32 × 1671 × 80171
LCM(48096,48102) = 385585632