What is the Least Common Multiple of 75760 and 75780?

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 75760 and 75780 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75760 and 75780, than apply into the LCM equation.

GCF(75760,75780) = 20
LCM(75760,75780) = ( 75760 × 75780) / 20
LCM(75760,75780) = 5741092800 / 20
LCM(75760,75780) = 287054640

Least Common Multiple (LCM) of 75760 and 75780 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75760 and 75780. First we will calculate the prime factors of 75760 and 75780.

Prime Factorization of 75760

Prime Factorization of 75780

Now multiplying the highest exponent prime factors to calculate the LCM of 75760 and 75780.

LCM(75760,75780) = 2⁴ × 5¹ × 947¹ × 3² × 421¹
LCM(75760,75780) = 287054640