What is the Least Common Multiple of 7728 and 7742?

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 7728 and 7742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7728 and 7742, than apply into the LCM equation.

GCF(7728,7742) = 14
LCM(7728,7742) = ( 7728 × 7742) / 14
LCM(7728,7742) = 59830176 / 14
LCM(7728,7742) = 4273584

Least Common Multiple (LCM) of 7728 and 7742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7728 and 7742. First we will calculate the prime factors of 7728 and 7742.

Prime Factorization of 7728

Prime Factorization of 7742

Now multiplying the highest exponent prime factors to calculate the LCM of 7728 and 7742.

LCM(7728,7742) = 2⁴ × 3¹ × 7² × 23¹ × 79¹
LCM(7728,7742) = 4273584