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What is the Least Common Multiple of 1003 and 1014?

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 1003 and 1014 is 1017042.

LCM(1003,1014) = 1017042

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Least Common Multiple of 1003 and 1014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1003 and 1014, than apply into the LCM equation.

GCF(1003,1014) = 1
LCM(1003,1014) = ( 1003 × 1014) / 1
LCM(1003,1014) = 1017042 / 1
LCM(1003,1014) = 1017042

Least Common Multiple (LCM) of 1003 and 1014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1003 and 1014. First we will calculate the prime factors of 1003 and 1014.

Prime Factorization of 1003

Prime factors of 1003 are 17, 59. Prime factorization of 1003 in exponential form is:

1003 = 171 × 591

Prime Factorization of 1014

Prime factors of 1014 are 2, 3, 13. Prime factorization of 1014 in exponential form is:

1014 = 21 × 31 × 132

Now multiplying the highest exponent prime factors to calculate the LCM of 1003 and 1014.

LCM(1003,1014) = 171 × 591 × 21 × 31 × 132
LCM(1003,1014) = 1017042