What is the Least Common Multiple of 31072 and 31080?

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 31072 and 31080 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31072 and 31080, than apply into the LCM equation.

GCF(31072,31080) = 8
LCM(31072,31080) = ( 31072 × 31080) / 8
LCM(31072,31080) = 965717760 / 8
LCM(31072,31080) = 120714720

Least Common Multiple (LCM) of 31072 and 31080 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31072 and 31080. First we will calculate the prime factors of 31072 and 31080.

Prime Factorization of 31072

Prime Factorization of 31080

Now multiplying the highest exponent prime factors to calculate the LCM of 31072 and 31080.

LCM(31072,31080) = 2⁵ × 971¹ × 3¹ × 5¹ × 7¹ × 37¹
LCM(31072,31080) = 120714720