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What is the Least Common Multiple of 31134 and 31146?

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 31134 and 31146 is 161616594.

LCM(31134,31146) = 161616594

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Least Common Multiple of 31134 and 31146 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31134 and 31146, than apply into the LCM equation.

GCF(31134,31146) = 6
LCM(31134,31146) = ( 31134 × 31146) / 6
LCM(31134,31146) = 969699564 / 6
LCM(31134,31146) = 161616594

Least Common Multiple (LCM) of 31134 and 31146 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31134 and 31146. First we will calculate the prime factors of 31134 and 31146.

Prime Factorization of 31134

Prime factors of 31134 are 2, 3, 5189. Prime factorization of 31134 in exponential form is:

31134 = 21 × 31 × 51891

Prime Factorization of 31146

Prime factors of 31146 are 2, 3, 29, 179. Prime factorization of 31146 in exponential form is:

31146 = 21 × 31 × 291 × 1791

Now multiplying the highest exponent prime factors to calculate the LCM of 31134 and 31146.

LCM(31134,31146) = 21 × 31 × 51891 × 291 × 1791
LCM(31134,31146) = 161616594