What is the Least Common Multiple of 31500 and 31520?

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 31500 and 31520 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31500 and 31520, than apply into the LCM equation.

GCF(31500,31520) = 20
LCM(31500,31520) = ( 31500 × 31520) / 20
LCM(31500,31520) = 992880000 / 20
LCM(31500,31520) = 49644000

Least Common Multiple (LCM) of 31500 and 31520 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31500 and 31520. First we will calculate the prime factors of 31500 and 31520.

Prime Factorization of 31500

Prime Factorization of 31520

Now multiplying the highest exponent prime factors to calculate the LCM of 31500 and 31520.

LCM(31500,31520) = 2⁵ × 3² × 5³ × 7¹ × 197¹
LCM(31500,31520) = 49644000