What is the Least Common Multiple of 1748 and 1752?

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 1748 and 1752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1748 and 1752, than apply into the LCM equation.

GCF(1748,1752) = 4
LCM(1748,1752) = ( 1748 × 1752) / 4
LCM(1748,1752) = 3062496 / 4
LCM(1748,1752) = 765624

Least Common Multiple (LCM) of 1748 and 1752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1748 and 1752. First we will calculate the prime factors of 1748 and 1752.

Prime Factorization of 1748

Prime Factorization of 1752

Now multiplying the highest exponent prime factors to calculate the LCM of 1748 and 1752.

LCM(1748,1752) = 2³ × 19¹ × 23¹ × 3¹ × 73¹
LCM(1748,1752) = 765624