What is the Least Common Multiple of 31506 and 31524?

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 31506 and 31524 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31506 and 31524, than apply into the LCM equation.

GCF(31506,31524) = 6
LCM(31506,31524) = ( 31506 × 31524) / 6
LCM(31506,31524) = 993195144 / 6
LCM(31506,31524) = 165532524

Least Common Multiple (LCM) of 31506 and 31524 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31506 and 31524. First we will calculate the prime factors of 31506 and 31524.

Prime Factorization of 31506

Prime Factorization of 31524

Now multiplying the highest exponent prime factors to calculate the LCM of 31506 and 31524.

LCM(31506,31524) = 2² × 3¹ × 59¹ × 89¹ × 37¹ × 71¹
LCM(31506,31524) = 165532524