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What is the Least Common Multiple of 30991 and 31003?

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 30991 and 31003 is 960813973.

LCM(30991,31003) = 960813973

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Least Common Multiple of 30991 and 31003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30991 and 31003, than apply into the LCM equation.

GCF(30991,31003) = 1
LCM(30991,31003) = ( 30991 × 31003) / 1
LCM(30991,31003) = 960813973 / 1
LCM(30991,31003) = 960813973

Least Common Multiple (LCM) of 30991 and 31003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30991 and 31003. First we will calculate the prime factors of 30991 and 31003.

Prime Factorization of 30991

Prime factors of 30991 are 17, 1823. Prime factorization of 30991 in exponential form is:

30991 = 171 × 18231

Prime Factorization of 31003

Prime factors of 31003 are 7, 43, 103. Prime factorization of 31003 in exponential form is:

31003 = 71 × 431 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 30991 and 31003.

LCM(30991,31003) = 171 × 18231 × 71 × 431 × 1031
LCM(30991,31003) = 960813973