What is the Least Common Multiple of 13900 and 13920?

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 13900 and 13920 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13900 and 13920, than apply into the LCM equation.

GCF(13900,13920) = 20
LCM(13900,13920) = ( 13900 × 13920) / 20
LCM(13900,13920) = 193488000 / 20
LCM(13900,13920) = 9674400

Least Common Multiple (LCM) of 13900 and 13920 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13900 and 13920. First we will calculate the prime factors of 13900 and 13920.

Prime Factorization of 13900

Prime Factorization of 13920

Now multiplying the highest exponent prime factors to calculate the LCM of 13900 and 13920.

LCM(13900,13920) = 2⁵ × 5² × 139¹ × 3¹ × 29¹
LCM(13900,13920) = 9674400