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What is the Least Common Multiple of 14003 and 14007?

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 14003 and 14007 is 196140021.

LCM(14003,14007) = 196140021

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Least Common Multiple of 14003 and 14007 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14003 and 14007, than apply into the LCM equation.

GCF(14003,14007) = 1
LCM(14003,14007) = ( 14003 × 14007) / 1
LCM(14003,14007) = 196140021 / 1
LCM(14003,14007) = 196140021

Least Common Multiple (LCM) of 14003 and 14007 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14003 and 14007. First we will calculate the prime factors of 14003 and 14007.

Prime Factorization of 14003

Prime factors of 14003 are 11, 19, 67. Prime factorization of 14003 in exponential form is:

14003 = 111 × 191 × 671

Prime Factorization of 14007

Prime factors of 14007 are 3, 7, 23, 29. Prime factorization of 14007 in exponential form is:

14007 = 31 × 71 × 231 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 14003 and 14007.

LCM(14003,14007) = 111 × 191 × 671 × 31 × 71 × 231 × 291
LCM(14003,14007) = 196140021