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What is the Least Common Multiple of 9991 and 10010?

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 9991 and 10010 is 100009910.

LCM(9991,10010) = 100009910

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Least Common Multiple of 9991 and 10010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9991 and 10010, than apply into the LCM equation.

GCF(9991,10010) = 1
LCM(9991,10010) = ( 9991 × 10010) / 1
LCM(9991,10010) = 100009910 / 1
LCM(9991,10010) = 100009910

Least Common Multiple (LCM) of 9991 and 10010 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9991 and 10010. First we will calculate the prime factors of 9991 and 10010.

Prime Factorization of 9991

Prime factors of 9991 are 97, 103. Prime factorization of 9991 in exponential form is:

9991 = 971 × 1031

Prime Factorization of 10010

Prime factors of 10010 are 2, 5, 7, 11, 13. Prime factorization of 10010 in exponential form is:

10010 = 21 × 51 × 71 × 111 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 9991 and 10010.

LCM(9991,10010) = 971 × 1031 × 21 × 51 × 71 × 111 × 131
LCM(9991,10010) = 100009910