What is the Least Common Multiple of 19104 and 19112?

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 19104 and 19112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19104 and 19112, than apply into the LCM equation.

GCF(19104,19112) = 8
LCM(19104,19112) = ( 19104 × 19112) / 8
LCM(19104,19112) = 365115648 / 8
LCM(19104,19112) = 45639456

Least Common Multiple (LCM) of 19104 and 19112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19104 and 19112. First we will calculate the prime factors of 19104 and 19112.

Prime Factorization of 19104

Prime Factorization of 19112

Now multiplying the highest exponent prime factors to calculate the LCM of 19104 and 19112.

LCM(19104,19112) = 2⁵ × 3¹ × 199¹ × 2389¹
LCM(19104,19112) = 45639456