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What is the Least Common Multiple of 31116 and 31125?

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 31116 and 31125 is 322828500.

LCM(31116,31125) = 322828500

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Least Common Multiple of 31116 and 31125 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31116 and 31125, than apply into the LCM equation.

GCF(31116,31125) = 3
LCM(31116,31125) = ( 31116 × 31125) / 3
LCM(31116,31125) = 968485500 / 3
LCM(31116,31125) = 322828500

Least Common Multiple (LCM) of 31116 and 31125 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31116 and 31125. First we will calculate the prime factors of 31116 and 31125.

Prime Factorization of 31116

Prime factors of 31116 are 2, 3, 2593. Prime factorization of 31116 in exponential form is:

31116 = 22 × 31 × 25931

Prime Factorization of 31125

Prime factors of 31125 are 3, 5, 83. Prime factorization of 31125 in exponential form is:

31125 = 31 × 53 × 831

Now multiplying the highest exponent prime factors to calculate the LCM of 31116 and 31125.

LCM(31116,31125) = 22 × 31 × 25931 × 53 × 831
LCM(31116,31125) = 322828500