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What is the Least Common Multiple of 57138 and 57152?

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 57138 and 57152 is 1632775488.

LCM(57138,57152) = 1632775488

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Least Common Multiple of 57138 and 57152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57138 and 57152, than apply into the LCM equation.

GCF(57138,57152) = 2
LCM(57138,57152) = ( 57138 × 57152) / 2
LCM(57138,57152) = 3265550976 / 2
LCM(57138,57152) = 1632775488

Least Common Multiple (LCM) of 57138 and 57152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57138 and 57152. First we will calculate the prime factors of 57138 and 57152.

Prime Factorization of 57138

Prime factors of 57138 are 2, 3, 89, 107. Prime factorization of 57138 in exponential form is:

57138 = 21 × 31 × 891 × 1071

Prime Factorization of 57152

Prime factors of 57152 are 2, 19, 47. Prime factorization of 57152 in exponential form is:

57152 = 26 × 191 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 57138 and 57152.

LCM(57138,57152) = 26 × 31 × 891 × 1071 × 191 × 471
LCM(57138,57152) = 1632775488