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What is the Least Common Multiple of 17744 and 17758?

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 17744 and 17758 is 157548976.

LCM(17744,17758) = 157548976

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Least Common Multiple of 17744 and 17758 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17744 and 17758, than apply into the LCM equation.

GCF(17744,17758) = 2
LCM(17744,17758) = ( 17744 × 17758) / 2
LCM(17744,17758) = 315097952 / 2
LCM(17744,17758) = 157548976

Least Common Multiple (LCM) of 17744 and 17758 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17744 and 17758. First we will calculate the prime factors of 17744 and 17758.

Prime Factorization of 17744

Prime factors of 17744 are 2, 1109. Prime factorization of 17744 in exponential form is:

17744 = 24 × 11091

Prime Factorization of 17758

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

17758 = 21 × 131 × 6831

Now multiplying the highest exponent prime factors to calculate the LCM of 17744 and 17758.

LCM(17744,17758) = 24 × 11091 × 131 × 6831
LCM(17744,17758) = 157548976