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What is the Least Common Multiple of 10010 and 10030?

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 10010 and 10030 is 10040030.

LCM(10010,10030) = 10040030

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Least Common Multiple of 10010 and 10030 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10010 and 10030, than apply into the LCM equation.

GCF(10010,10030) = 10
LCM(10010,10030) = ( 10010 × 10030) / 10
LCM(10010,10030) = 100400300 / 10
LCM(10010,10030) = 10040030

Least Common Multiple (LCM) of 10010 and 10030 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10010 and 10030. First we will calculate the prime factors of 10010 and 10030.

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

Prime Factorization of 10030

Prime factors of 10030 are 2, 5, 17, 59. Prime factorization of 10030 in exponential form is:

10030 = 21 × 51 × 171 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 10010 and 10030.

LCM(10010,10030) = 21 × 51 × 71 × 111 × 131 × 171 × 591
LCM(10010,10030) = 10040030