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What is the Least Common Multiple of 5414 and 5424?

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 5414 and 5424 is 14682768.

LCM(5414,5424) = 14682768

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Least Common Multiple of 5414 and 5424 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5414 and 5424, than apply into the LCM equation.

GCF(5414,5424) = 2
LCM(5414,5424) = ( 5414 × 5424) / 2
LCM(5414,5424) = 29365536 / 2
LCM(5414,5424) = 14682768

Least Common Multiple (LCM) of 5414 and 5424 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5414 and 5424. First we will calculate the prime factors of 5414 and 5424.

Prime Factorization of 5414

Prime factors of 5414 are 2, 2707. Prime factorization of 5414 in exponential form is:

5414 = 21 × 27071

Prime Factorization of 5424

Prime factors of 5424 are 2, 3, 113. Prime factorization of 5424 in exponential form is:

5424 = 24 × 31 × 1131

Now multiplying the highest exponent prime factors to calculate the LCM of 5414 and 5424.

LCM(5414,5424) = 24 × 27071 × 31 × 1131
LCM(5414,5424) = 14682768