What is the Least Common Multiple of 75960 and 75980?

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 75960 and 75980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75960 and 75980, than apply into the LCM equation.

GCF(75960,75980) = 20
LCM(75960,75980) = ( 75960 × 75980) / 20
LCM(75960,75980) = 5771440800 / 20
LCM(75960,75980) = 288572040

Least Common Multiple (LCM) of 75960 and 75980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75960 and 75980. First we will calculate the prime factors of 75960 and 75980.

Prime Factorization of 75960

Prime Factorization of 75980

Now multiplying the highest exponent prime factors to calculate the LCM of 75960 and 75980.

LCM(75960,75980) = 2³ × 3² × 5¹ × 211¹ × 29¹ × 131¹
LCM(75960,75980) = 288572040