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What is the Least Common Multiple of 31310 and 31324?

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 31310 and 31324 is 490377220.

LCM(31310,31324) = 490377220

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Least Common Multiple of 31310 and 31324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31310 and 31324, than apply into the LCM equation.

GCF(31310,31324) = 2
LCM(31310,31324) = ( 31310 × 31324) / 2
LCM(31310,31324) = 980754440 / 2
LCM(31310,31324) = 490377220

Least Common Multiple (LCM) of 31310 and 31324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31310 and 31324. First we will calculate the prime factors of 31310 and 31324.

Prime Factorization of 31310

Prime factors of 31310 are 2, 5, 31, 101. Prime factorization of 31310 in exponential form is:

31310 = 21 × 51 × 311 × 1011

Prime Factorization of 31324

Prime factors of 31324 are 2, 41, 191. Prime factorization of 31324 in exponential form is:

31324 = 22 × 411 × 1911

Now multiplying the highest exponent prime factors to calculate the LCM of 31310 and 31324.

LCM(31310,31324) = 22 × 51 × 311 × 1011 × 411 × 1911
LCM(31310,31324) = 490377220