What is the Least Common Multiple of 31344 and 31356?

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 31356 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 31356, than apply into the LCM equation.

GCF(31344,31356) = 12
LCM(31344,31356) = ( 31344 × 31356) / 12
LCM(31344,31356) = 982822464 / 12
LCM(31344,31356) = 81901872

Least Common Multiple (LCM) of 31344 and 31356 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31344 and 31356. First we will calculate the prime factors of 31344 and 31356.

Prime Factorization of 31344

Prime Factorization of 31356

Now multiplying the highest exponent prime factors to calculate the LCM of 31344 and 31356.

LCM(31344,31356) = 2⁴ × 3² × 653¹ × 13¹ × 67¹
LCM(31344,31356) = 81901872