What is the Least Common Multiple of 13872 and 13880?

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 13872 and 13880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13872 and 13880, than apply into the LCM equation.

GCF(13872,13880) = 8
LCM(13872,13880) = ( 13872 × 13880) / 8
LCM(13872,13880) = 192543360 / 8
LCM(13872,13880) = 24067920

Least Common Multiple (LCM) of 13872 and 13880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13872 and 13880. First we will calculate the prime factors of 13872 and 13880.

Prime Factorization of 13872

Prime Factorization of 13880

Now multiplying the highest exponent prime factors to calculate the LCM of 13872 and 13880.

LCM(13872,13880) = 2⁴ × 3¹ × 17² × 5¹ × 347¹
LCM(13872,13880) = 24067920