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What is the Least Common Multiple of 8305 and 8320?

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 8305 and 8320 is 13819520.

LCM(8305,8320) = 13819520

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Least Common Multiple of 8305 and 8320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8305 and 8320, than apply into the LCM equation.

GCF(8305,8320) = 5
LCM(8305,8320) = ( 8305 × 8320) / 5
LCM(8305,8320) = 69097600 / 5
LCM(8305,8320) = 13819520

Least Common Multiple (LCM) of 8305 and 8320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8305 and 8320. First we will calculate the prime factors of 8305 and 8320.

Prime Factorization of 8305

Prime factors of 8305 are 5, 11, 151. Prime factorization of 8305 in exponential form is:

8305 = 51 × 111 × 1511

Prime Factorization of 8320

Prime factors of 8320 are 2, 5, 13. Prime factorization of 8320 in exponential form is:

8320 = 27 × 51 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 8305 and 8320.

LCM(8305,8320) = 51 × 111 × 1511 × 27 × 131
LCM(8305,8320) = 13819520