What is the Least Common Multiple of 31344 and 31364?

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 of 31344 and 31364 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31344 and 31364, than apply into the LCM equation.

GCF(31344,31364) = 4
LCM(31344,31364) = ( 31344 × 31364) / 4
LCM(31344,31364) = 983073216 / 4
LCM(31344,31364) = 245768304

Least Common Multiple (LCM) of 31344 and 31364 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31344 and 31364. First we will calculate the prime factors of 31344 and 31364.

Prime Factorization of 31344

Prime Factorization of 31364

Now multiplying the highest exponent prime factors to calculate the LCM of 31344 and 31364.

LCM(31344,31364) = 2⁴ × 3¹ × 653¹ × 7841¹
LCM(31344,31364) = 245768304