What is the Least Common Multiple of 75684 and 75696?

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 75684 and 75696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75684 and 75696, than apply into the LCM equation.

GCF(75684,75696) = 12
LCM(75684,75696) = ( 75684 × 75696) / 12
LCM(75684,75696) = 5728976064 / 12
LCM(75684,75696) = 477414672

Least Common Multiple (LCM) of 75684 and 75696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75684 and 75696. First we will calculate the prime factors of 75684 and 75696.

Prime Factorization of 75684

Prime Factorization of 75696

Now multiplying the highest exponent prime factors to calculate the LCM of 75684 and 75696.

LCM(75684,75696) = 2⁴ × 3¹ × 7¹ × 17¹ × 53¹ × 19¹ × 83¹
LCM(75684,75696) = 477414672