What is the Least Common Multiple of 1728 and 1745?

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 1745 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 1745, than apply into the LCM equation.

GCF(1728,1745) = 1
LCM(1728,1745) = ( 1728 × 1745) / 1
LCM(1728,1745) = 3015360 / 1
LCM(1728,1745) = 3015360

Least Common Multiple (LCM) of 1728 and 1745 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1728 and 1745. First we will calculate the prime factors of 1728 and 1745.

Prime Factorization of 1728

Prime Factorization of 1745

Now multiplying the highest exponent prime factors to calculate the LCM of 1728 and 1745.

LCM(1728,1745) = 2⁶ × 3³ × 5¹ × 349¹
LCM(1728,1745) = 3015360