What is the Least Common Multiple of 19104 and 19120?

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 19120 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 19120, than apply into the LCM equation.

GCF(19104,19120) = 16
LCM(19104,19120) = ( 19104 × 19120) / 16
LCM(19104,19120) = 365268480 / 16
LCM(19104,19120) = 22829280

Least Common Multiple (LCM) of 19104 and 19120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19104 and 19120. First we will calculate the prime factors of 19104 and 19120.

Prime Factorization of 19104

Prime Factorization of 19120

Now multiplying the highest exponent prime factors to calculate the LCM of 19104 and 19120.

LCM(19104,19120) = 2⁵ × 3¹ × 199¹ × 5¹ × 239¹
LCM(19104,19120) = 22829280