What is the Least Common Multiple of 19860 and 19872?

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 19860 and 19872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19860 and 19872, than apply into the LCM equation.

GCF(19860,19872) = 12
LCM(19860,19872) = ( 19860 × 19872) / 12
LCM(19860,19872) = 394657920 / 12
LCM(19860,19872) = 32888160

Least Common Multiple (LCM) of 19860 and 19872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19860 and 19872. First we will calculate the prime factors of 19860 and 19872.

Prime Factorization of 19860

Prime Factorization of 19872

Now multiplying the highest exponent prime factors to calculate the LCM of 19860 and 19872.

LCM(19860,19872) = 2⁵ × 3³ × 5¹ × 331¹ × 23¹
LCM(19860,19872) = 32888160