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What is the Least Common Multiple of 31306 and 31310?

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 31306 and 31310 is 490095430.

LCM(31306,31310) = 490095430

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Least Common Multiple of 31306 and 31310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31306 and 31310, than apply into the LCM equation.

GCF(31306,31310) = 2
LCM(31306,31310) = ( 31306 × 31310) / 2
LCM(31306,31310) = 980190860 / 2
LCM(31306,31310) = 490095430

Least Common Multiple (LCM) of 31306 and 31310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31306 and 31310. First we will calculate the prime factors of 31306 and 31310.

Prime Factorization of 31306

Prime factors of 31306 are 2, 11, 1423. Prime factorization of 31306 in exponential form is:

31306 = 21 × 111 × 14231

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

Now multiplying the highest exponent prime factors to calculate the LCM of 31306 and 31310.

LCM(31306,31310) = 21 × 111 × 14231 × 51 × 311 × 1011
LCM(31306,31310) = 490095430