What is the Least Common Multiple of 19152 and 19164?

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 19152 and 19164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19152 and 19164, than apply into the LCM equation.

GCF(19152,19164) = 12
LCM(19152,19164) = ( 19152 × 19164) / 12
LCM(19152,19164) = 367028928 / 12
LCM(19152,19164) = 30585744

Least Common Multiple (LCM) of 19152 and 19164 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19152 and 19164. First we will calculate the prime factors of 19152 and 19164.

Prime Factorization of 19152

Prime Factorization of 19164

Now multiplying the highest exponent prime factors to calculate the LCM of 19152 and 19164.

LCM(19152,19164) = 2⁴ × 3² × 7¹ × 19¹ × 1597¹
LCM(19152,19164) = 30585744