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What is the Least Common Multiple of 13400 and 13420?

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 13400 and 13420 is 8991400.

LCM(13400,13420) = 8991400

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Least Common Multiple of 13400 and 13420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13400 and 13420, than apply into the LCM equation.

GCF(13400,13420) = 20
LCM(13400,13420) = ( 13400 × 13420) / 20
LCM(13400,13420) = 179828000 / 20
LCM(13400,13420) = 8991400

Least Common Multiple (LCM) of 13400 and 13420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13400 and 13420. First we will calculate the prime factors of 13400 and 13420.

Prime Factorization of 13400

Prime factors of 13400 are 2, 5, 67. Prime factorization of 13400 in exponential form is:

13400 = 23 × 52 × 671

Prime Factorization of 13420

Prime factors of 13420 are 2, 5, 11, 61. Prime factorization of 13420 in exponential form is:

13420 = 22 × 51 × 111 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 13400 and 13420.

LCM(13400,13420) = 23 × 52 × 671 × 111 × 611
LCM(13400,13420) = 8991400