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What is the Least Common Multiple of 12390 and 12408?

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 12390 and 12408 is 25622520.

LCM(12390,12408) = 25622520

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Least Common Multiple of 12390 and 12408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12390 and 12408, than apply into the LCM equation.

GCF(12390,12408) = 6
LCM(12390,12408) = ( 12390 × 12408) / 6
LCM(12390,12408) = 153735120 / 6
LCM(12390,12408) = 25622520

Least Common Multiple (LCM) of 12390 and 12408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12390 and 12408. First we will calculate the prime factors of 12390 and 12408.

Prime Factorization of 12390

Prime factors of 12390 are 2, 3, 5, 7, 59. Prime factorization of 12390 in exponential form is:

12390 = 21 × 31 × 51 × 71 × 591

Prime Factorization of 12408

Prime factors of 12408 are 2, 3, 11, 47. Prime factorization of 12408 in exponential form is:

12408 = 23 × 31 × 111 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 12390 and 12408.

LCM(12390,12408) = 23 × 31 × 51 × 71 × 591 × 111 × 471
LCM(12390,12408) = 25622520