What is the Least Common Multiple of 13860 and 13872?

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 13860 and 13872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13860 and 13872, than apply into the LCM equation.

GCF(13860,13872) = 12
LCM(13860,13872) = ( 13860 × 13872) / 12
LCM(13860,13872) = 192265920 / 12
LCM(13860,13872) = 16022160

Least Common Multiple (LCM) of 13860 and 13872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13860 and 13872. First we will calculate the prime factors of 13860 and 13872.

Prime Factorization of 13860

Prime Factorization of 13872

Now multiplying the highest exponent prime factors to calculate the LCM of 13860 and 13872.

LCM(13860,13872) = 2⁴ × 3² × 5¹ × 7¹ × 11¹ × 17²
LCM(13860,13872) = 16022160