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What is the Least Common Multiple of 29994 and 30009?

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 29994 and 30009 is 300029982.

LCM(29994,30009) = 300029982

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Least Common Multiple of 29994 and 30009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29994 and 30009, than apply into the LCM equation.

GCF(29994,30009) = 3
LCM(29994,30009) = ( 29994 × 30009) / 3
LCM(29994,30009) = 900089946 / 3
LCM(29994,30009) = 300029982

Least Common Multiple (LCM) of 29994 and 30009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29994 and 30009. First we will calculate the prime factors of 29994 and 30009.

Prime Factorization of 29994

Prime factors of 29994 are 2, 3, 4999. Prime factorization of 29994 in exponential form is:

29994 = 21 × 31 × 49991

Prime Factorization of 30009

Prime factors of 30009 are 3, 7, 1429. Prime factorization of 30009 in exponential form is:

30009 = 31 × 71 × 14291

Now multiplying the highest exponent prime factors to calculate the LCM of 29994 and 30009.

LCM(29994,30009) = 21 × 31 × 49991 × 71 × 14291
LCM(29994,30009) = 300029982