What is the Least Common Multiple of 13875 and 13890?

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 13875 and 13890 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13875 and 13890, than apply into the LCM equation.

GCF(13875,13890) = 15
LCM(13875,13890) = ( 13875 × 13890) / 15
LCM(13875,13890) = 192723750 / 15
LCM(13875,13890) = 12848250

Least Common Multiple (LCM) of 13875 and 13890 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13875 and 13890. First we will calculate the prime factors of 13875 and 13890.

Prime Factorization of 13875

Prime Factorization of 13890

Now multiplying the highest exponent prime factors to calculate the LCM of 13875 and 13890.

LCM(13875,13890) = 3¹ × 5³ × 37¹ × 2¹ × 463¹
LCM(13875,13890) = 12848250