What is the Least Common Multiple of 1742 and 1748?

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 1742 and 1748 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1742 and 1748, than apply into the LCM equation.

GCF(1742,1748) = 2
LCM(1742,1748) = ( 1742 × 1748) / 2
LCM(1742,1748) = 3045016 / 2
LCM(1742,1748) = 1522508

Least Common Multiple (LCM) of 1742 and 1748 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1742 and 1748. First we will calculate the prime factors of 1742 and 1748.

Prime Factorization of 1742

Prime Factorization of 1748

Now multiplying the highest exponent prime factors to calculate the LCM of 1742 and 1748.

LCM(1742,1748) = 2² × 13¹ × 67¹ × 19¹ × 23¹
LCM(1742,1748) = 1522508