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What is the Least Common Multiple of 5185 and 5200?

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 5185 and 5200 is 5392400.

LCM(5185,5200) = 5392400

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Least Common Multiple of 5185 and 5200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5185 and 5200, than apply into the LCM equation.

GCF(5185,5200) = 5
LCM(5185,5200) = ( 5185 × 5200) / 5
LCM(5185,5200) = 26962000 / 5
LCM(5185,5200) = 5392400

Least Common Multiple (LCM) of 5185 and 5200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5185 and 5200. First we will calculate the prime factors of 5185 and 5200.

Prime Factorization of 5185

Prime factors of 5185 are 5, 17, 61. Prime factorization of 5185 in exponential form is:

5185 = 51 × 171 × 611

Prime Factorization of 5200

Prime factors of 5200 are 2, 5, 13. Prime factorization of 5200 in exponential form is:

5200 = 24 × 52 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 5185 and 5200.

LCM(5185,5200) = 52 × 171 × 611 × 24 × 131
LCM(5185,5200) = 5392400