What is the Least Common Multiple of 72075 and 72080?

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 72075 and 72080 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72075 and 72080, than apply into the LCM equation.

GCF(72075,72080) = 5
LCM(72075,72080) = ( 72075 × 72080) / 5
LCM(72075,72080) = 5195166000 / 5
LCM(72075,72080) = 1039033200

Least Common Multiple (LCM) of 72075 and 72080 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72075 and 72080. First we will calculate the prime factors of 72075 and 72080.

Prime Factorization of 72075

Prime Factorization of 72080

Now multiplying the highest exponent prime factors to calculate the LCM of 72075 and 72080.

LCM(72075,72080) = 3¹ × 5² × 31² × 2⁴ × 17¹ × 53¹
LCM(72075,72080) = 1039033200