What is the Least Common Multiple of 31530 and 31536?

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 31530 and 31536 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31530 and 31536, than apply into the LCM equation.

GCF(31530,31536) = 6
LCM(31530,31536) = ( 31530 × 31536) / 6
LCM(31530,31536) = 994330080 / 6
LCM(31530,31536) = 165721680

Least Common Multiple (LCM) of 31530 and 31536 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31530 and 31536. First we will calculate the prime factors of 31530 and 31536.

Prime Factorization of 31530

Prime Factorization of 31536

Now multiplying the highest exponent prime factors to calculate the LCM of 31530 and 31536.

LCM(31530,31536) = 2⁴ × 3³ × 5¹ × 1051¹ × 73¹
LCM(31530,31536) = 165721680