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What is the Least Common Multiple of 25100 and 25120?

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 25100 and 25120 is 31525600.

LCM(25100,25120) = 31525600

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Least Common Multiple of 25100 and 25120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25100 and 25120, than apply into the LCM equation.

GCF(25100,25120) = 20
LCM(25100,25120) = ( 25100 × 25120) / 20
LCM(25100,25120) = 630512000 / 20
LCM(25100,25120) = 31525600

Least Common Multiple (LCM) of 25100 and 25120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25100 and 25120. First we will calculate the prime factors of 25100 and 25120.

Prime Factorization of 25100

Prime factors of 25100 are 2, 5, 251. Prime factorization of 25100 in exponential form is:

25100 = 22 × 52 × 2511

Prime Factorization of 25120

Prime factors of 25120 are 2, 5, 157. Prime factorization of 25120 in exponential form is:

25120 = 25 × 51 × 1571

Now multiplying the highest exponent prime factors to calculate the LCM of 25100 and 25120.

LCM(25100,25120) = 25 × 52 × 2511 × 1571
LCM(25100,25120) = 31525600