What is the Least Common Multiple of 31590 and 31599?

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 31590 and 31599 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31590 and 31599, than apply into the LCM equation.

GCF(31590,31599) = 9
LCM(31590,31599) = ( 31590 × 31599) / 9
LCM(31590,31599) = 998212410 / 9
LCM(31590,31599) = 110912490

Least Common Multiple (LCM) of 31590 and 31599 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31590 and 31599. First we will calculate the prime factors of 31590 and 31599.

Prime Factorization of 31590

Prime Factorization of 31599

Now multiplying the highest exponent prime factors to calculate the LCM of 31590 and 31599.

LCM(31590,31599) = 2¹ × 3⁵ × 5¹ × 13¹ × 3511¹
LCM(31590,31599) = 110912490