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What is the Least Common Multiple of 5398 and 5408?

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 5398 and 5408 is 14596192.

LCM(5398,5408) = 14596192

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Least Common Multiple of 5398 and 5408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5398 and 5408, than apply into the LCM equation.

GCF(5398,5408) = 2
LCM(5398,5408) = ( 5398 × 5408) / 2
LCM(5398,5408) = 29192384 / 2
LCM(5398,5408) = 14596192

Least Common Multiple (LCM) of 5398 and 5408 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5398 and 5408. First we will calculate the prime factors of 5398 and 5408.

Prime Factorization of 5398

Prime factors of 5398 are 2, 2699. Prime factorization of 5398 in exponential form is:

5398 = 21 × 26991

Prime Factorization of 5408

Prime factors of 5408 are 2, 13. Prime factorization of 5408 in exponential form is:

5408 = 25 × 132

Now multiplying the highest exponent prime factors to calculate the LCM of 5398 and 5408.

LCM(5398,5408) = 25 × 26991 × 132
LCM(5398,5408) = 14596192