What is the Least Common Multiple of 10075 and 10080?

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 10075 and 10080 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10075 and 10080, than apply into the LCM equation.

GCF(10075,10080) = 5
LCM(10075,10080) = ( 10075 × 10080) / 5
LCM(10075,10080) = 101556000 / 5
LCM(10075,10080) = 20311200

Least Common Multiple (LCM) of 10075 and 10080 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10075 and 10080. First we will calculate the prime factors of 10075 and 10080.

Prime Factorization of 10075

Prime Factorization of 10080

Now multiplying the highest exponent prime factors to calculate the LCM of 10075 and 10080.

LCM(10075,10080) = 5² × 13¹ × 31¹ × 2⁵ × 3² × 7¹
LCM(10075,10080) = 20311200