What is the Least Common Multiple of 75684 and 75688?

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 75688 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 75688, than apply into the LCM equation.

GCF(75684,75688) = 4
LCM(75684,75688) = ( 75684 × 75688) / 4
LCM(75684,75688) = 5728370592 / 4
LCM(75684,75688) = 1432092648

Least Common Multiple (LCM) of 75684 and 75688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75684 and 75688. First we will calculate the prime factors of 75684 and 75688.

Prime Factorization of 75684

Prime Factorization of 75688

Now multiplying the highest exponent prime factors to calculate the LCM of 75684 and 75688.

LCM(75684,75688) = 2³ × 3¹ × 7¹ × 17¹ × 53¹ × 9461¹
LCM(75684,75688) = 1432092648