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What is the Least Common Multiple of 31006 and 31020?

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 31006 and 31020 is 480903060.

LCM(31006,31020) = 480903060

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Least Common Multiple of 31006 and 31020 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31006 and 31020, than apply into the LCM equation.

GCF(31006,31020) = 2
LCM(31006,31020) = ( 31006 × 31020) / 2
LCM(31006,31020) = 961806120 / 2
LCM(31006,31020) = 480903060

Least Common Multiple (LCM) of 31006 and 31020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31006 and 31020. First we will calculate the prime factors of 31006 and 31020.

Prime Factorization of 31006

Prime factors of 31006 are 2, 37, 419. Prime factorization of 31006 in exponential form is:

31006 = 21 × 371 × 4191

Prime Factorization of 31020

Prime factors of 31020 are 2, 3, 5, 11, 47. Prime factorization of 31020 in exponential form is:

31020 = 22 × 31 × 51 × 111 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 31006 and 31020.

LCM(31006,31020) = 22 × 371 × 4191 × 31 × 51 × 111 × 471
LCM(31006,31020) = 480903060