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What is the Least Common Multiple of 13986 and 14003?

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 13986 and 14003 is 195845958.

LCM(13986,14003) = 195845958

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Least Common Multiple of 13986 and 14003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13986 and 14003, than apply into the LCM equation.

GCF(13986,14003) = 1
LCM(13986,14003) = ( 13986 × 14003) / 1
LCM(13986,14003) = 195845958 / 1
LCM(13986,14003) = 195845958

Least Common Multiple (LCM) of 13986 and 14003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13986 and 14003. First we will calculate the prime factors of 13986 and 14003.

Prime Factorization of 13986

Prime factors of 13986 are 2, 3, 7, 37. Prime factorization of 13986 in exponential form is:

13986 = 21 × 33 × 71 × 371

Prime Factorization of 14003

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

14003 = 111 × 191 × 671

Now multiplying the highest exponent prime factors to calculate the LCM of 13986 and 14003.

LCM(13986,14003) = 21 × 33 × 71 × 371 × 111 × 191 × 671
LCM(13986,14003) = 195845958