What is the Least Common Multiple of 5688 and 5696?

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 5688 and 5696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5688 and 5696, than apply into the LCM equation.

GCF(5688,5696) = 8
LCM(5688,5696) = ( 5688 × 5696) / 8
LCM(5688,5696) = 32398848 / 8
LCM(5688,5696) = 4049856

Least Common Multiple (LCM) of 5688 and 5696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5688 and 5696. First we will calculate the prime factors of 5688 and 5696.

Prime Factorization of 5688

Prime Factorization of 5696

Now multiplying the highest exponent prime factors to calculate the LCM of 5688 and 5696.

LCM(5688,5696) = 2⁶ × 3² × 79¹ × 89¹
LCM(5688,5696) = 4049856