GCF and LCM Calculator Logo

What is the Least Common Multiple of 13830 and 13842?

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 (LCM) of 13830 and 13842 is 31905810.

LCM(13830,13842) = 31905810

LCM Calculator and
and

Least Common Multiple of 13830 and 13842 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 13842, than apply into the LCM equation.

GCF(13830,13842) = 6
LCM(13830,13842) = ( 13830 × 13842) / 6
LCM(13830,13842) = 191434860 / 6
LCM(13830,13842) = 31905810

Least Common Multiple (LCM) of 13830 and 13842 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13830 and 13842. First we will calculate the prime factors of 13830 and 13842.

Prime Factorization of 13830

Prime factors of 13830 are 2, 3, 5, 461. Prime factorization of 13830 in exponential form is:

13830 = 21 × 31 × 51 × 4611

Prime Factorization of 13842

Prime factors of 13842 are 2, 3, 769. Prime factorization of 13842 in exponential form is:

13842 = 21 × 32 × 7691

Now multiplying the highest exponent prime factors to calculate the LCM of 13830 and 13842.

LCM(13830,13842) = 21 × 32 × 51 × 4611 × 7691
LCM(13830,13842) = 31905810