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What is the Least Common Multiple of 13221 and 13238?

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 13221 and 13238 is 175019598.

LCM(13221,13238) = 175019598

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Least Common Multiple of 13221 and 13238 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13221 and 13238, than apply into the LCM equation.

GCF(13221,13238) = 1
LCM(13221,13238) = ( 13221 × 13238) / 1
LCM(13221,13238) = 175019598 / 1
LCM(13221,13238) = 175019598

Least Common Multiple (LCM) of 13221 and 13238 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13221 and 13238. First we will calculate the prime factors of 13221 and 13238.

Prime Factorization of 13221

Prime factors of 13221 are 3, 13, 113. Prime factorization of 13221 in exponential form is:

13221 = 32 × 131 × 1131

Prime Factorization of 13238

Prime factors of 13238 are 2, 6619. Prime factorization of 13238 in exponential form is:

13238 = 21 × 66191

Now multiplying the highest exponent prime factors to calculate the LCM of 13221 and 13238.

LCM(13221,13238) = 32 × 131 × 1131 × 21 × 66191
LCM(13221,13238) = 175019598