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What is the Least Common Multiple of 31005 and 31022?

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 31005 and 31022 is 961837110.

LCM(31005,31022) = 961837110

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Least Common Multiple of 31005 and 31022 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31005 and 31022, than apply into the LCM equation.

GCF(31005,31022) = 1
LCM(31005,31022) = ( 31005 × 31022) / 1
LCM(31005,31022) = 961837110 / 1
LCM(31005,31022) = 961837110

Least Common Multiple (LCM) of 31005 and 31022 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31005 and 31022. First we will calculate the prime factors of 31005 and 31022.

Prime Factorization of 31005

Prime factors of 31005 are 3, 5, 13, 53. Prime factorization of 31005 in exponential form is:

31005 = 32 × 51 × 131 × 531

Prime Factorization of 31022

Prime factors of 31022 are 2, 15511. Prime factorization of 31022 in exponential form is:

31022 = 21 × 155111

Now multiplying the highest exponent prime factors to calculate the LCM of 31005 and 31022.

LCM(31005,31022) = 32 × 51 × 131 × 531 × 21 × 155111
LCM(31005,31022) = 961837110