What is the Least Common Multiple of 75744 and 75760?

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 75744 and 75760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75744 and 75760, than apply into the LCM equation.

GCF(75744,75760) = 16
LCM(75744,75760) = ( 75744 × 75760) / 16
LCM(75744,75760) = 5738365440 / 16
LCM(75744,75760) = 358647840

Least Common Multiple (LCM) of 75744 and 75760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75744 and 75760. First we will calculate the prime factors of 75744 and 75760.

Prime Factorization of 75744

Prime Factorization of 75760

Now multiplying the highest exponent prime factors to calculate the LCM of 75744 and 75760.

LCM(75744,75760) = 2⁵ × 3² × 263¹ × 5¹ × 947¹
LCM(75744,75760) = 358647840