What is the Least Common Multiple of 750 and 759?

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 750 and 759 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 750 and 759, than apply into the LCM equation.

GCF(750,759) = 3
LCM(750,759) = ( 750 × 759) / 3
LCM(750,759) = 569250 / 3
LCM(750,759) = 189750

Least Common Multiple (LCM) of 750 and 759 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 750 and 759. First we will calculate the prime factors of 750 and 759.

Prime Factorization of 750

Prime Factorization of 759

Now multiplying the highest exponent prime factors to calculate the LCM of 750 and 759.

LCM(750,759) = 2¹ × 3¹ × 5³ × 11¹ × 23¹
LCM(750,759) = 189750