What is the Least Common Multiple of 19524 and 19536?

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 19524 and 19536 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19524 and 19536, than apply into the LCM equation.

GCF(19524,19536) = 12
LCM(19524,19536) = ( 19524 × 19536) / 12
LCM(19524,19536) = 381420864 / 12
LCM(19524,19536) = 31785072

Least Common Multiple (LCM) of 19524 and 19536 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19524 and 19536. First we will calculate the prime factors of 19524 and 19536.

Prime Factorization of 19524

Prime Factorization of 19536

Now multiplying the highest exponent prime factors to calculate the LCM of 19524 and 19536.

LCM(19524,19536) = 2⁴ × 3¹ × 1627¹ × 11¹ × 37¹
LCM(19524,19536) = 31785072