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What is the Least Common Multiple of 17574 and 17578?

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 17574 and 17578 is 154457886.

LCM(17574,17578) = 154457886

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Least Common Multiple of 17574 and 17578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17574 and 17578, than apply into the LCM equation.

GCF(17574,17578) = 2
LCM(17574,17578) = ( 17574 × 17578) / 2
LCM(17574,17578) = 308915772 / 2
LCM(17574,17578) = 154457886

Least Common Multiple (LCM) of 17574 and 17578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17574 and 17578. First we will calculate the prime factors of 17574 and 17578.

Prime Factorization of 17574

Prime factors of 17574 are 2, 3, 29, 101. Prime factorization of 17574 in exponential form is:

17574 = 21 × 31 × 291 × 1011

Prime Factorization of 17578

Prime factors of 17578 are 2, 11, 17, 47. Prime factorization of 17578 in exponential form is:

17578 = 21 × 111 × 171 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 17574 and 17578.

LCM(17574,17578) = 21 × 31 × 291 × 1011 × 111 × 171 × 471
LCM(17574,17578) = 154457886