What is the Least Common Multiple of 19728 and 19734?

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 19728 and 19734 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19728 and 19734, than apply into the LCM equation.

GCF(19728,19734) = 6
LCM(19728,19734) = ( 19728 × 19734) / 6
LCM(19728,19734) = 389312352 / 6
LCM(19728,19734) = 64885392

Least Common Multiple (LCM) of 19728 and 19734 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19728 and 19734. First we will calculate the prime factors of 19728 and 19734.

Prime Factorization of 19728

Prime Factorization of 19734

Now multiplying the highest exponent prime factors to calculate the LCM of 19728 and 19734.

LCM(19728,19734) = 2⁴ × 3² × 137¹ × 11¹ × 13¹ × 23¹
LCM(19728,19734) = 64885392