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What is the Least Common Multiple of 13413 and 13422?

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 13413 and 13422 is 60009762.

LCM(13413,13422) = 60009762

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Least Common Multiple of 13413 and 13422 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13413 and 13422, than apply into the LCM equation.

GCF(13413,13422) = 3
LCM(13413,13422) = ( 13413 × 13422) / 3
LCM(13413,13422) = 180029286 / 3
LCM(13413,13422) = 60009762

Least Common Multiple (LCM) of 13413 and 13422 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13413 and 13422. First we will calculate the prime factors of 13413 and 13422.

Prime Factorization of 13413

Prime factors of 13413 are 3, 17, 263. Prime factorization of 13413 in exponential form is:

13413 = 31 × 171 × 2631

Prime Factorization of 13422

Prime factors of 13422 are 2, 3, 2237. Prime factorization of 13422 in exponential form is:

13422 = 21 × 31 × 22371

Now multiplying the highest exponent prime factors to calculate the LCM of 13413 and 13422.

LCM(13413,13422) = 31 × 171 × 2631 × 21 × 22371
LCM(13413,13422) = 60009762