What is the Least Common Multiple of 1710 and 1728?

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 1710 and 1728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1710 and 1728, than apply into the LCM equation.

GCF(1710,1728) = 18
LCM(1710,1728) = ( 1710 × 1728) / 18
LCM(1710,1728) = 2954880 / 18
LCM(1710,1728) = 164160

Least Common Multiple (LCM) of 1710 and 1728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1710 and 1728. First we will calculate the prime factors of 1710 and 1728.

Prime Factorization of 1710

Prime Factorization of 1728

Now multiplying the highest exponent prime factors to calculate the LCM of 1710 and 1728.

LCM(1710,1728) = 2⁶ × 3³ × 5¹ × 19¹
LCM(1710,1728) = 164160