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What is the Least Common Multiple of 1705 and 1716?

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 1705 and 1716 is 265980.

LCM(1705,1716) = 265980

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Least Common Multiple of 1705 and 1716 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1705 and 1716, than apply into the LCM equation.

GCF(1705,1716) = 11
LCM(1705,1716) = ( 1705 × 1716) / 11
LCM(1705,1716) = 2925780 / 11
LCM(1705,1716) = 265980

Least Common Multiple (LCM) of 1705 and 1716 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1705 and 1716. First we will calculate the prime factors of 1705 and 1716.

Prime Factorization of 1705

Prime factors of 1705 are 5, 11, 31. Prime factorization of 1705 in exponential form is:

1705 = 51 × 111 × 311

Prime Factorization of 1716

Prime factors of 1716 are 2, 3, 11, 13. Prime factorization of 1716 in exponential form is:

1716 = 22 × 31 × 111 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 1705 and 1716.

LCM(1705,1716) = 51 × 111 × 311 × 22 × 31 × 131
LCM(1705,1716) = 265980