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What is the Least Common Multiple of 31294 and 31312?

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 31294 and 31312 is 489938864.

LCM(31294,31312) = 489938864

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Least Common Multiple of 31294 and 31312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31294 and 31312, than apply into the LCM equation.

GCF(31294,31312) = 2
LCM(31294,31312) = ( 31294 × 31312) / 2
LCM(31294,31312) = 979877728 / 2
LCM(31294,31312) = 489938864

Least Common Multiple (LCM) of 31294 and 31312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31294 and 31312. First we will calculate the prime factors of 31294 and 31312.

Prime Factorization of 31294

Prime factors of 31294 are 2, 15647. Prime factorization of 31294 in exponential form is:

31294 = 21 × 156471

Prime Factorization of 31312

Prime factors of 31312 are 2, 19, 103. Prime factorization of 31312 in exponential form is:

31312 = 24 × 191 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 31294 and 31312.

LCM(31294,31312) = 24 × 156471 × 191 × 1031
LCM(31294,31312) = 489938864