What is the Least Common Multiple of 75600 and 75614?

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 75600 and 75614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75600 and 75614, than apply into the LCM equation.

GCF(75600,75614) = 14
LCM(75600,75614) = ( 75600 × 75614) / 14
LCM(75600,75614) = 5716418400 / 14
LCM(75600,75614) = 408315600

Least Common Multiple (LCM) of 75600 and 75614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75600 and 75614. First we will calculate the prime factors of 75600 and 75614.

Prime Factorization of 75600

Prime Factorization of 75614

Now multiplying the highest exponent prime factors to calculate the LCM of 75600 and 75614.

LCM(75600,75614) = 2⁴ × 3³ × 5² × 7¹ × 11¹ × 491¹
LCM(75600,75614) = 408315600