What is the Least Common Multiple of 728 and 746?

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 728 and 746 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 728 and 746, than apply into the LCM equation.

GCF(728,746) = 2
LCM(728,746) = ( 728 × 746) / 2
LCM(728,746) = 543088 / 2
LCM(728,746) = 271544

Least Common Multiple (LCM) of 728 and 746 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 728 and 746. First we will calculate the prime factors of 728 and 746.

Prime Factorization of 728

Prime Factorization of 746

Now multiplying the highest exponent prime factors to calculate the LCM of 728 and 746.

LCM(728,746) = 2³ × 7¹ × 13¹ × 373¹
LCM(728,746) = 271544