What is the Least Common Multiple of 19872 and 19888?

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 19872 and 19888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19872 and 19888, than apply into the LCM equation.

GCF(19872,19888) = 16
LCM(19872,19888) = ( 19872 × 19888) / 16
LCM(19872,19888) = 395214336 / 16
LCM(19872,19888) = 24700896

Least Common Multiple (LCM) of 19872 and 19888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19872 and 19888. First we will calculate the prime factors of 19872 and 19888.

Prime Factorization of 19872

Prime Factorization of 19888

Now multiplying the highest exponent prime factors to calculate the LCM of 19872 and 19888.

LCM(19872,19888) = 2⁵ × 3³ × 23¹ × 11¹ × 113¹
LCM(19872,19888) = 24700896