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What is the Least Common Multiple of 31180 and 31200?

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 31180 and 31200 is 48640800.

LCM(31180,31200) = 48640800

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Least Common Multiple of 31180 and 31200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31180 and 31200, than apply into the LCM equation.

GCF(31180,31200) = 20
LCM(31180,31200) = ( 31180 × 31200) / 20
LCM(31180,31200) = 972816000 / 20
LCM(31180,31200) = 48640800

Least Common Multiple (LCM) of 31180 and 31200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31180 and 31200. First we will calculate the prime factors of 31180 and 31200.

Prime Factorization of 31180

Prime factors of 31180 are 2, 5, 1559. Prime factorization of 31180 in exponential form is:

31180 = 22 × 51 × 15591

Prime Factorization of 31200

Prime factors of 31200 are 2, 3, 5, 13. Prime factorization of 31200 in exponential form is:

31200 = 25 × 31 × 52 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 31180 and 31200.

LCM(31180,31200) = 25 × 52 × 15591 × 31 × 131
LCM(31180,31200) = 48640800