What is the Least Common Multiple of 13965 and 13980?

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 13965 and 13980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13965 and 13980, than apply into the LCM equation.

GCF(13965,13980) = 15
LCM(13965,13980) = ( 13965 × 13980) / 15
LCM(13965,13980) = 195230700 / 15
LCM(13965,13980) = 13015380

Least Common Multiple (LCM) of 13965 and 13980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13965 and 13980. First we will calculate the prime factors of 13965 and 13980.

Prime Factorization of 13965

Prime Factorization of 13980

Now multiplying the highest exponent prime factors to calculate the LCM of 13965 and 13980.

LCM(13965,13980) = 3¹ × 5¹ × 7² × 19¹ × 2² × 233¹
LCM(13965,13980) = 13015380