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What is the Least Common Multiple of 5194 and 5213?

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 5194 and 5213 is 27076322.

LCM(5194,5213) = 27076322

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Least Common Multiple of 5194 and 5213 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5194 and 5213, than apply into the LCM equation.

GCF(5194,5213) = 1
LCM(5194,5213) = ( 5194 × 5213) / 1
LCM(5194,5213) = 27076322 / 1
LCM(5194,5213) = 27076322

Least Common Multiple (LCM) of 5194 and 5213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5194 and 5213. First we will calculate the prime factors of 5194 and 5213.

Prime Factorization of 5194

Prime factors of 5194 are 2, 7, 53. Prime factorization of 5194 in exponential form is:

5194 = 21 × 72 × 531

Prime Factorization of 5213

Prime factors of 5213 are 13, 401. Prime factorization of 5213 in exponential form is:

5213 = 131 × 4011

Now multiplying the highest exponent prime factors to calculate the LCM of 5194 and 5213.

LCM(5194,5213) = 21 × 72 × 531 × 131 × 4011
LCM(5194,5213) = 27076322