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What is the Least Common Multiple of 31160 and 31164?

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 31160 and 31164 is 242767560.

LCM(31160,31164) = 242767560

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Least Common Multiple of 31160 and 31164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31160 and 31164, than apply into the LCM equation.

GCF(31160,31164) = 4
LCM(31160,31164) = ( 31160 × 31164) / 4
LCM(31160,31164) = 971070240 / 4
LCM(31160,31164) = 242767560

Least Common Multiple (LCM) of 31160 and 31164 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31160 and 31164. First we will calculate the prime factors of 31160 and 31164.

Prime Factorization of 31160

Prime factors of 31160 are 2, 5, 19, 41. Prime factorization of 31160 in exponential form is:

31160 = 23 × 51 × 191 × 411

Prime Factorization of 31164

Prime factors of 31164 are 2, 3, 7, 53. Prime factorization of 31164 in exponential form is:

31164 = 22 × 31 × 72 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 31160 and 31164.

LCM(31160,31164) = 23 × 51 × 191 × 411 × 31 × 72 × 531
LCM(31160,31164) = 242767560