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What is the Least Common Multiple of 57120 and 57125?

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 57120 and 57125 is 652596000.

LCM(57120,57125) = 652596000

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Least Common Multiple of 57120 and 57125 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57120 and 57125, than apply into the LCM equation.

GCF(57120,57125) = 5
LCM(57120,57125) = ( 57120 × 57125) / 5
LCM(57120,57125) = 3262980000 / 5
LCM(57120,57125) = 652596000

Least Common Multiple (LCM) of 57120 and 57125 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57120 and 57125. First we will calculate the prime factors of 57120 and 57125.

Prime Factorization of 57120

Prime factors of 57120 are 2, 3, 5, 7, 17. Prime factorization of 57120 in exponential form is:

57120 = 25 × 31 × 51 × 71 × 171

Prime Factorization of 57125

Prime factors of 57125 are 5, 457. Prime factorization of 57125 in exponential form is:

57125 = 53 × 4571

Now multiplying the highest exponent prime factors to calculate the LCM of 57120 and 57125.

LCM(57120,57125) = 25 × 31 × 53 × 71 × 171 × 4571
LCM(57120,57125) = 652596000