What is the Least Common Multiple of 69744 and 69750?

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 69744 and 69750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69744 and 69750, than apply into the LCM equation.

GCF(69744,69750) = 6
LCM(69744,69750) = ( 69744 × 69750) / 6
LCM(69744,69750) = 4864644000 / 6
LCM(69744,69750) = 810774000

Least Common Multiple (LCM) of 69744 and 69750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69744 and 69750. First we will calculate the prime factors of 69744 and 69750.

Prime Factorization of 69744

Prime Factorization of 69750

Now multiplying the highest exponent prime factors to calculate the LCM of 69744 and 69750.

LCM(69744,69750) = 2⁴ × 3² × 1453¹ × 5³ × 31¹
LCM(69744,69750) = 810774000