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What is the Least Common Multiple of 25700 and 25720?

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 25700 and 25720 is 33050200.

LCM(25700,25720) = 33050200

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Least Common Multiple of 25700 and 25720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25700 and 25720, than apply into the LCM equation.

GCF(25700,25720) = 20
LCM(25700,25720) = ( 25700 × 25720) / 20
LCM(25700,25720) = 661004000 / 20
LCM(25700,25720) = 33050200

Least Common Multiple (LCM) of 25700 and 25720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25700 and 25720. First we will calculate the prime factors of 25700 and 25720.

Prime Factorization of 25700

Prime factors of 25700 are 2, 5, 257. Prime factorization of 25700 in exponential form is:

25700 = 22 × 52 × 2571

Prime Factorization of 25720

Prime factors of 25720 are 2, 5, 643. Prime factorization of 25720 in exponential form is:

25720 = 23 × 51 × 6431

Now multiplying the highest exponent prime factors to calculate the LCM of 25700 and 25720.

LCM(25700,25720) = 23 × 52 × 2571 × 6431
LCM(25700,25720) = 33050200