What is the Least Common Multiple of 19728 and 19745?

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 19745 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 19745, than apply into the LCM equation.

GCF(19728,19745) = 1
LCM(19728,19745) = ( 19728 × 19745) / 1
LCM(19728,19745) = 389529360 / 1
LCM(19728,19745) = 389529360

Least Common Multiple (LCM) of 19728 and 19745 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19728 and 19745. First we will calculate the prime factors of 19728 and 19745.

Prime Factorization of 19728

Prime Factorization of 19745

Now multiplying the highest exponent prime factors to calculate the LCM of 19728 and 19745.

LCM(19728,19745) = 2⁴ × 3² × 137¹ × 5¹ × 11¹ × 359¹
LCM(19728,19745) = 389529360