What is the Least Common Multiple of 31120 and 31140?

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 31120 and 31140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31120 and 31140, than apply into the LCM equation.

GCF(31120,31140) = 20
LCM(31120,31140) = ( 31120 × 31140) / 20
LCM(31120,31140) = 969076800 / 20
LCM(31120,31140) = 48453840

Least Common Multiple (LCM) of 31120 and 31140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31120 and 31140. First we will calculate the prime factors of 31120 and 31140.

Prime Factorization of 31120

Prime Factorization of 31140

Now multiplying the highest exponent prime factors to calculate the LCM of 31120 and 31140.

LCM(31120,31140) = 2⁴ × 5¹ × 389¹ × 3² × 173¹
LCM(31120,31140) = 48453840