What is the Least Common Multiple of 75738 and 75744?

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 75738 and 75744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75738 and 75744, than apply into the LCM equation.

GCF(75738,75744) = 6
LCM(75738,75744) = ( 75738 × 75744) / 6
LCM(75738,75744) = 5736699072 / 6
LCM(75738,75744) = 956116512

Least Common Multiple (LCM) of 75738 and 75744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75738 and 75744. First we will calculate the prime factors of 75738 and 75744.

Prime Factorization of 75738

Prime Factorization of 75744

Now multiplying the highest exponent prime factors to calculate the LCM of 75738 and 75744.

LCM(75738,75744) = 2⁵ × 3² × 13¹ × 971¹ × 263¹
LCM(75738,75744) = 956116512