What is the Least Common Multiple of 75665 and 75680?

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 75665 and 75680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75665 and 75680, than apply into the LCM equation.

GCF(75665,75680) = 5
LCM(75665,75680) = ( 75665 × 75680) / 5
LCM(75665,75680) = 5726327200 / 5
LCM(75665,75680) = 1145265440

Least Common Multiple (LCM) of 75665 and 75680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75665 and 75680. First we will calculate the prime factors of 75665 and 75680.

Prime Factorization of 75665

Prime Factorization of 75680

Now multiplying the highest exponent prime factors to calculate the LCM of 75665 and 75680.

LCM(75665,75680) = 5¹ × 37¹ × 409¹ × 2⁵ × 11¹ × 43¹
LCM(75665,75680) = 1145265440