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What is the Least Common Multiple of 18990 and 19000?

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 18990 and 19000 is 36081000.

LCM(18990,19000) = 36081000

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Least Common Multiple of 18990 and 19000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18990 and 19000, than apply into the LCM equation.

GCF(18990,19000) = 10
LCM(18990,19000) = ( 18990 × 19000) / 10
LCM(18990,19000) = 360810000 / 10
LCM(18990,19000) = 36081000

Least Common Multiple (LCM) of 18990 and 19000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18990 and 19000. First we will calculate the prime factors of 18990 and 19000.

Prime Factorization of 18990

Prime factors of 18990 are 2, 3, 5, 211. Prime factorization of 18990 in exponential form is:

18990 = 21 × 32 × 51 × 2111

Prime Factorization of 19000

Prime factors of 19000 are 2, 5, 19. Prime factorization of 19000 in exponential form is:

19000 = 23 × 53 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 18990 and 19000.

LCM(18990,19000) = 23 × 32 × 53 × 2111 × 191
LCM(18990,19000) = 36081000