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What is the Least Common Multiple of 17980 and 17990?

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 17980 and 17990 is 32346020.

LCM(17980,17990) = 32346020

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Least Common Multiple of 17980 and 17990 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17980 and 17990, than apply into the LCM equation.

GCF(17980,17990) = 10
LCM(17980,17990) = ( 17980 × 17990) / 10
LCM(17980,17990) = 323460200 / 10
LCM(17980,17990) = 32346020

Least Common Multiple (LCM) of 17980 and 17990 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17980 and 17990. First we will calculate the prime factors of 17980 and 17990.

Prime Factorization of 17980

Prime factors of 17980 are 2, 5, 29, 31. Prime factorization of 17980 in exponential form is:

17980 = 22 × 51 × 291 × 311

Prime Factorization of 17990

Prime factors of 17990 are 2, 5, 7, 257. Prime factorization of 17990 in exponential form is:

17990 = 21 × 51 × 71 × 2571

Now multiplying the highest exponent prime factors to calculate the LCM of 17980 and 17990.

LCM(17980,17990) = 22 × 51 × 291 × 311 × 71 × 2571
LCM(17980,17990) = 32346020