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What is the Least Common Multiple of 17966 and 17974?

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 17966 and 17974 is 161460442.

LCM(17966,17974) = 161460442

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Least Common Multiple of 17966 and 17974 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17966 and 17974, than apply into the LCM equation.

GCF(17966,17974) = 2
LCM(17966,17974) = ( 17966 × 17974) / 2
LCM(17966,17974) = 322920884 / 2
LCM(17966,17974) = 161460442

Least Common Multiple (LCM) of 17966 and 17974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17966 and 17974. First we will calculate the prime factors of 17966 and 17974.

Prime Factorization of 17966

Prime factors of 17966 are 2, 13, 691. Prime factorization of 17966 in exponential form is:

17966 = 21 × 131 × 6911

Prime Factorization of 17974

Prime factors of 17974 are 2, 11, 19, 43. Prime factorization of 17974 in exponential form is:

17974 = 21 × 111 × 191 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 17966 and 17974.

LCM(17966,17974) = 21 × 131 × 6911 × 111 × 191 × 431
LCM(17966,17974) = 161460442