What is the Least Common Multiple of 750 and 754?

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 754 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 754, than apply into the LCM equation.

GCF(750,754) = 2
LCM(750,754) = ( 750 × 754) / 2
LCM(750,754) = 565500 / 2
LCM(750,754) = 282750

Least Common Multiple (LCM) of 750 and 754 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 750 and 754. First we will calculate the prime factors of 750 and 754.

Prime Factorization of 750

Prime Factorization of 754

Now multiplying the highest exponent prime factors to calculate the LCM of 750 and 754.

LCM(750,754) = 2¹ × 3¹ × 5³ × 13¹ × 29¹
LCM(750,754) = 282750