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What is the Least Common Multiple of 17757 and 17769?

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 17757 and 17769 is 105174711.

LCM(17757,17769) = 105174711

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Least Common Multiple of 17757 and 17769 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17757 and 17769, than apply into the LCM equation.

GCF(17757,17769) = 3
LCM(17757,17769) = ( 17757 × 17769) / 3
LCM(17757,17769) = 315524133 / 3
LCM(17757,17769) = 105174711

Least Common Multiple (LCM) of 17757 and 17769 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17757 and 17769. First we will calculate the prime factors of 17757 and 17769.

Prime Factorization of 17757

Prime factors of 17757 are 3, 1973. Prime factorization of 17757 in exponential form is:

17757 = 32 × 19731

Prime Factorization of 17769

Prime factors of 17769 are 3, 5923. Prime factorization of 17769 in exponential form is:

17769 = 31 × 59231

Now multiplying the highest exponent prime factors to calculate the LCM of 17757 and 17769.

LCM(17757,17769) = 32 × 19731 × 59231
LCM(17757,17769) = 105174711