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What is the Least Common Multiple of 9744 and 9758?

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 9744 and 9758 is 6791568.

LCM(9744,9758) = 6791568

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Least Common Multiple of 9744 and 9758 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9744 and 9758, than apply into the LCM equation.

GCF(9744,9758) = 14
LCM(9744,9758) = ( 9744 × 9758) / 14
LCM(9744,9758) = 95081952 / 14
LCM(9744,9758) = 6791568

Least Common Multiple (LCM) of 9744 and 9758 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9744 and 9758. First we will calculate the prime factors of 9744 and 9758.

Prime Factorization of 9744

Prime factors of 9744 are 2, 3, 7, 29. Prime factorization of 9744 in exponential form is:

9744 = 24 × 31 × 71 × 291

Prime Factorization of 9758

Prime factors of 9758 are 2, 7, 17, 41. Prime factorization of 9758 in exponential form is:

9758 = 21 × 71 × 171 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 9744 and 9758.

LCM(9744,9758) = 24 × 31 × 71 × 291 × 171 × 411
LCM(9744,9758) = 6791568