What is the Least Common Multiple of 78075 and 78090?

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 78075 and 78090 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78075 and 78090, than apply into the LCM equation.

GCF(78075,78090) = 15
LCM(78075,78090) = ( 78075 × 78090) / 15
LCM(78075,78090) = 6096876750 / 15
LCM(78075,78090) = 406458450

Least Common Multiple (LCM) of 78075 and 78090 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78075 and 78090. First we will calculate the prime factors of 78075 and 78090.

Prime Factorization of 78075

Prime Factorization of 78090

Now multiplying the highest exponent prime factors to calculate the LCM of 78075 and 78090.

LCM(78075,78090) = 3² × 5² × 347¹ × 2¹ × 19¹ × 137¹
LCM(78075,78090) = 406458450