What is the Least Common Multiple of 75870 and 75880?

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 75870 and 75880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75870 and 75880, than apply into the LCM equation.

GCF(75870,75880) = 10
LCM(75870,75880) = ( 75870 × 75880) / 10
LCM(75870,75880) = 5757015600 / 10
LCM(75870,75880) = 575701560

Least Common Multiple (LCM) of 75870 and 75880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75870 and 75880. First we will calculate the prime factors of 75870 and 75880.

Prime Factorization of 75870

Prime Factorization of 75880

Now multiplying the highest exponent prime factors to calculate the LCM of 75870 and 75880.

LCM(75870,75880) = 2³ × 3³ × 5¹ × 281¹ × 7¹ × 271¹
LCM(75870,75880) = 575701560