What is the Least Common Multiple of 1728 and 1746?

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 1728 and 1746 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1728 and 1746, than apply into the LCM equation.

GCF(1728,1746) = 18
LCM(1728,1746) = ( 1728 × 1746) / 18
LCM(1728,1746) = 3017088 / 18
LCM(1728,1746) = 167616

Least Common Multiple (LCM) of 1728 and 1746 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1746. First we will calculate the prime factors of 1728 and 1746.

Prime Factorization of 1728

Prime Factorization of 1746

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1746.

LCM(1728,1746) = 2⁶ × 3³ × 97¹
LCM(1728,1746) = 167616