What is the Least Common Multiple of 1725 and 1740?

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 1725 and 1740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1725 and 1740, than apply into the LCM equation.

GCF(1725,1740) = 15
LCM(1725,1740) = ( 1725 × 1740) / 15
LCM(1725,1740) = 3001500 / 15
LCM(1725,1740) = 200100

Least Common Multiple (LCM) of 1725 and 1740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1725 and 1740. First we will calculate the prime factors of 1725 and 1740.

Prime Factorization of 1725

Prime Factorization of 1740

Now multiplying the highest exponent prime factors to calculate the LCM of 1725 and 1740.

LCM(1725,1740) = 3¹ × 5² × 23¹ × 2² × 29¹
LCM(1725,1740) = 200100