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What is the Least Common Multiple of 17758 and 17765?

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 17758 and 17765 is 315470870.

LCM(17758,17765) = 315470870

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Least Common Multiple of 17758 and 17765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17758 and 17765, than apply into the LCM equation.

GCF(17758,17765) = 1
LCM(17758,17765) = ( 17758 × 17765) / 1
LCM(17758,17765) = 315470870 / 1
LCM(17758,17765) = 315470870

Least Common Multiple (LCM) of 17758 and 17765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17758 and 17765. First we will calculate the prime factors of 17758 and 17765.

Prime Factorization of 17758

Prime factors of 17758 are 2, 13, 683. Prime factorization of 17758 in exponential form is:

17758 = 21 × 131 × 6831

Prime Factorization of 17765

Prime factors of 17765 are 5, 11, 17, 19. Prime factorization of 17765 in exponential form is:

17765 = 51 × 111 × 171 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 17758 and 17765.

LCM(17758,17765) = 21 × 131 × 6831 × 51 × 111 × 171 × 191
LCM(17758,17765) = 315470870