What is the Least Common Multiple of 13830 and 13845?

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 13830 and 13845 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13830 and 13845, than apply into the LCM equation.

GCF(13830,13845) = 15
LCM(13830,13845) = ( 13830 × 13845) / 15
LCM(13830,13845) = 191476350 / 15
LCM(13830,13845) = 12765090

Least Common Multiple (LCM) of 13830 and 13845 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13830 and 13845. First we will calculate the prime factors of 13830 and 13845.

Prime Factorization of 13830

Prime Factorization of 13845

Now multiplying the highest exponent prime factors to calculate the LCM of 13830 and 13845.

LCM(13830,13845) = 2¹ × 3¹ × 5¹ × 461¹ × 13¹ × 71¹
LCM(13830,13845) = 12765090