What is the Least Common Multiple of 31758 and 31772?

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 31758 and 31772 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31758 and 31772, than apply into the LCM equation.

GCF(31758,31772) = 2
LCM(31758,31772) = ( 31758 × 31772) / 2
LCM(31758,31772) = 1009015176 / 2
LCM(31758,31772) = 504507588

Least Common Multiple (LCM) of 31758 and 31772 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31758 and 31772. First we will calculate the prime factors of 31758 and 31772.

Prime Factorization of 31758

Prime Factorization of 31772

Now multiplying the highest exponent prime factors to calculate the LCM of 31758 and 31772.

LCM(31758,31772) = 2² × 3¹ × 67¹ × 79¹ × 13² × 47¹
LCM(31758,31772) = 504507588