What is the Least Common Multiple of 19875 and 19880?

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 19875 and 19880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19875 and 19880, than apply into the LCM equation.

GCF(19875,19880) = 5
LCM(19875,19880) = ( 19875 × 19880) / 5
LCM(19875,19880) = 395115000 / 5
LCM(19875,19880) = 79023000

Least Common Multiple (LCM) of 19875 and 19880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19875 and 19880. First we will calculate the prime factors of 19875 and 19880.

Prime Factorization of 19875

Prime Factorization of 19880

Now multiplying the highest exponent prime factors to calculate the LCM of 19875 and 19880.

LCM(19875,19880) = 3¹ × 5³ × 53¹ × 2³ × 7¹ × 71¹
LCM(19875,19880) = 79023000