What is the Least Common Multiple of 67744 and 67752?

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 67744 and 67752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67744 and 67752, than apply into the LCM equation.

GCF(67744,67752) = 8
LCM(67744,67752) = ( 67744 × 67752) / 8
LCM(67744,67752) = 4589791488 / 8
LCM(67744,67752) = 573723936

Least Common Multiple (LCM) of 67744 and 67752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67744 and 67752. First we will calculate the prime factors of 67744 and 67752.

Prime Factorization of 67744

Prime Factorization of 67752

Now multiplying the highest exponent prime factors to calculate the LCM of 67744 and 67752.

LCM(67744,67752) = 2⁵ × 29¹ × 73¹ × 3² × 941¹
LCM(67744,67752) = 573723936