What is the Least Common Multiple of 1734 and 1742?

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 1734 and 1742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1734 and 1742, than apply into the LCM equation.

GCF(1734,1742) = 2
LCM(1734,1742) = ( 1734 × 1742) / 2
LCM(1734,1742) = 3020628 / 2
LCM(1734,1742) = 1510314

Least Common Multiple (LCM) of 1734 and 1742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1734 and 1742. First we will calculate the prime factors of 1734 and 1742.

Prime Factorization of 1734

Prime Factorization of 1742

Now multiplying the highest exponent prime factors to calculate the LCM of 1734 and 1742.

LCM(1734,1742) = 2¹ × 3¹ × 17² × 13¹ × 67¹
LCM(1734,1742) = 1510314