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What is the Least Common Multiple of 29998 and 30003?

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 29998 and 30003 is 900029994.

LCM(29998,30003) = 900029994

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Least Common Multiple of 29998 and 30003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29998 and 30003, than apply into the LCM equation.

GCF(29998,30003) = 1
LCM(29998,30003) = ( 29998 × 30003) / 1
LCM(29998,30003) = 900029994 / 1
LCM(29998,30003) = 900029994

Least Common Multiple (LCM) of 29998 and 30003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29998 and 30003. First we will calculate the prime factors of 29998 and 30003.

Prime Factorization of 29998

Prime factors of 29998 are 2, 53, 283. Prime factorization of 29998 in exponential form is:

29998 = 21 × 531 × 2831

Prime Factorization of 30003

Prime factors of 30003 are 3, 73, 137. Prime factorization of 30003 in exponential form is:

30003 = 31 × 731 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 29998 and 30003.

LCM(29998,30003) = 21 × 531 × 2831 × 31 × 731 × 1371
LCM(29998,30003) = 900029994