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What is the Least Common Multiple of 31056 and 31070?

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 31056 and 31070 is 482454960.

LCM(31056,31070) = 482454960

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Least Common Multiple of 31056 and 31070 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31056 and 31070, than apply into the LCM equation.

GCF(31056,31070) = 2
LCM(31056,31070) = ( 31056 × 31070) / 2
LCM(31056,31070) = 964909920 / 2
LCM(31056,31070) = 482454960

Least Common Multiple (LCM) of 31056 and 31070 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31056 and 31070. First we will calculate the prime factors of 31056 and 31070.

Prime Factorization of 31056

Prime factors of 31056 are 2, 3, 647. Prime factorization of 31056 in exponential form is:

31056 = 24 × 31 × 6471

Prime Factorization of 31070

Prime factors of 31070 are 2, 5, 13, 239. Prime factorization of 31070 in exponential form is:

31070 = 21 × 51 × 131 × 2391

Now multiplying the highest exponent prime factors to calculate the LCM of 31056 and 31070.

LCM(31056,31070) = 24 × 31 × 6471 × 51 × 131 × 2391
LCM(31056,31070) = 482454960