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What is the Least Common Multiple of 5205 and 5216?

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 5205 and 5216 is 27149280.

LCM(5205,5216) = 27149280

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Least Common Multiple of 5205 and 5216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5205 and 5216, than apply into the LCM equation.

GCF(5205,5216) = 1
LCM(5205,5216) = ( 5205 × 5216) / 1
LCM(5205,5216) = 27149280 / 1
LCM(5205,5216) = 27149280

Least Common Multiple (LCM) of 5205 and 5216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5205 and 5216. First we will calculate the prime factors of 5205 and 5216.

Prime Factorization of 5205

Prime factors of 5205 are 3, 5, 347. Prime factorization of 5205 in exponential form is:

5205 = 31 × 51 × 3471

Prime Factorization of 5216

Prime factors of 5216 are 2, 163. Prime factorization of 5216 in exponential form is:

5216 = 25 × 1631

Now multiplying the highest exponent prime factors to calculate the LCM of 5205 and 5216.

LCM(5205,5216) = 31 × 51 × 3471 × 25 × 1631
LCM(5205,5216) = 27149280