What is the Least Common Multiple of 45870 and 45880?

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 45870 and 45880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45870 and 45880, than apply into the LCM equation.

GCF(45870,45880) = 10
LCM(45870,45880) = ( 45870 × 45880) / 10
LCM(45870,45880) = 2104515600 / 10
LCM(45870,45880) = 210451560

Least Common Multiple (LCM) of 45870 and 45880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45870 and 45880. First we will calculate the prime factors of 45870 and 45880.

Prime Factorization of 45870

Prime Factorization of 45880

Now multiplying the highest exponent prime factors to calculate the LCM of 45870 and 45880.

LCM(45870,45880) = 2³ × 3¹ × 5¹ × 11¹ × 139¹ × 31¹ × 37¹
LCM(45870,45880) = 210451560