What is the Least Common Multiple of 19734 and 19742?

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 19734 and 19742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19734 and 19742, than apply into the LCM equation.

GCF(19734,19742) = 2
LCM(19734,19742) = ( 19734 × 19742) / 2
LCM(19734,19742) = 389588628 / 2
LCM(19734,19742) = 194794314

Least Common Multiple (LCM) of 19734 and 19742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19734 and 19742. First we will calculate the prime factors of 19734 and 19742.

Prime Factorization of 19734

Prime Factorization of 19742

Now multiplying the highest exponent prime factors to calculate the LCM of 19734 and 19742.

LCM(19734,19742) = 2¹ × 3¹ × 11¹ × 13¹ × 23¹ × 9871¹
LCM(19734,19742) = 194794314