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What is the Least Common Multiple of 18408 and 18420?

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 18408 and 18420 is 28256280.

LCM(18408,18420) = 28256280

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Least Common Multiple of 18408 and 18420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18408 and 18420, than apply into the LCM equation.

GCF(18408,18420) = 12
LCM(18408,18420) = ( 18408 × 18420) / 12
LCM(18408,18420) = 339075360 / 12
LCM(18408,18420) = 28256280

Least Common Multiple (LCM) of 18408 and 18420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18408 and 18420. First we will calculate the prime factors of 18408 and 18420.

Prime Factorization of 18408

Prime factors of 18408 are 2, 3, 13, 59. Prime factorization of 18408 in exponential form is:

18408 = 23 × 31 × 131 × 591

Prime Factorization of 18420

Prime factors of 18420 are 2, 3, 5, 307. Prime factorization of 18420 in exponential form is:

18420 = 22 × 31 × 51 × 3071

Now multiplying the highest exponent prime factors to calculate the LCM of 18408 and 18420.

LCM(18408,18420) = 23 × 31 × 131 × 591 × 51 × 3071
LCM(18408,18420) = 28256280