What is the Least Common Multiple of 31080 and 31100?

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 31080 and 31100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31080 and 31100, than apply into the LCM equation.

GCF(31080,31100) = 20
LCM(31080,31100) = ( 31080 × 31100) / 20
LCM(31080,31100) = 966588000 / 20
LCM(31080,31100) = 48329400

Least Common Multiple (LCM) of 31080 and 31100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31080 and 31100. First we will calculate the prime factors of 31080 and 31100.

Prime Factorization of 31080

Prime Factorization of 31100

Now multiplying the highest exponent prime factors to calculate the LCM of 31080 and 31100.

LCM(31080,31100) = 2³ × 3¹ × 5² × 7¹ × 37¹ × 311¹
LCM(31080,31100) = 48329400