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What is the Least Common Multiple of 29991 and 30004?

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 29991 and 30004 is 69219228.

LCM(29991,30004) = 69219228

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Least Common Multiple of 29991 and 30004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29991 and 30004, than apply into the LCM equation.

GCF(29991,30004) = 13
LCM(29991,30004) = ( 29991 × 30004) / 13
LCM(29991,30004) = 899849964 / 13
LCM(29991,30004) = 69219228

Least Common Multiple (LCM) of 29991 and 30004 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29991 and 30004. First we will calculate the prime factors of 29991 and 30004.

Prime Factorization of 29991

Prime factors of 29991 are 3, 13, 769. Prime factorization of 29991 in exponential form is:

29991 = 31 × 131 × 7691

Prime Factorization of 30004

Prime factors of 30004 are 2, 13, 577. Prime factorization of 30004 in exponential form is:

30004 = 22 × 131 × 5771

Now multiplying the highest exponent prime factors to calculate the LCM of 29991 and 30004.

LCM(29991,30004) = 31 × 131 × 7691 × 22 × 5771
LCM(29991,30004) = 69219228