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What is the Least Common Multiple of 9735 and 9741?

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 9735 and 9741 is 31609545.

LCM(9735,9741) = 31609545

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Least Common Multiple of 9735 and 9741 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9735 and 9741, than apply into the LCM equation.

GCF(9735,9741) = 3
LCM(9735,9741) = ( 9735 × 9741) / 3
LCM(9735,9741) = 94828635 / 3
LCM(9735,9741) = 31609545

Least Common Multiple (LCM) of 9735 and 9741 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9735 and 9741. First we will calculate the prime factors of 9735 and 9741.

Prime Factorization of 9735

Prime factors of 9735 are 3, 5, 11, 59. Prime factorization of 9735 in exponential form is:

9735 = 31 × 51 × 111 × 591

Prime Factorization of 9741

Prime factors of 9741 are 3, 17, 191. Prime factorization of 9741 in exponential form is:

9741 = 31 × 171 × 1911

Now multiplying the highest exponent prime factors to calculate the LCM of 9735 and 9741.

LCM(9735,9741) = 31 × 51 × 111 × 591 × 171 × 1911
LCM(9735,9741) = 31609545