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What is the Least Common Multiple of 57306 and 57320?

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 57306 and 57320 is 1642389960.

LCM(57306,57320) = 1642389960

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Least Common Multiple of 57306 and 57320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57306 and 57320, than apply into the LCM equation.

GCF(57306,57320) = 2
LCM(57306,57320) = ( 57306 × 57320) / 2
LCM(57306,57320) = 3284779920 / 2
LCM(57306,57320) = 1642389960

Least Common Multiple (LCM) of 57306 and 57320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57306 and 57320. First we will calculate the prime factors of 57306 and 57320.

Prime Factorization of 57306

Prime factors of 57306 are 2, 3, 9551. Prime factorization of 57306 in exponential form is:

57306 = 21 × 31 × 95511

Prime Factorization of 57320

Prime factors of 57320 are 2, 5, 1433. Prime factorization of 57320 in exponential form is:

57320 = 23 × 51 × 14331

Now multiplying the highest exponent prime factors to calculate the LCM of 57306 and 57320.

LCM(57306,57320) = 23 × 31 × 95511 × 51 × 14331
LCM(57306,57320) = 1642389960