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What is the Least Common Multiple of 13996 and 14008?

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 13996 and 14008 is 49013992.

LCM(13996,14008) = 49013992

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Least Common Multiple of 13996 and 14008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13996 and 14008, than apply into the LCM equation.

GCF(13996,14008) = 4
LCM(13996,14008) = ( 13996 × 14008) / 4
LCM(13996,14008) = 196055968 / 4
LCM(13996,14008) = 49013992

Least Common Multiple (LCM) of 13996 and 14008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13996 and 14008. First we will calculate the prime factors of 13996 and 14008.

Prime Factorization of 13996

Prime factors of 13996 are 2, 3499. Prime factorization of 13996 in exponential form is:

13996 = 22 × 34991

Prime Factorization of 14008

Prime factors of 14008 are 2, 17, 103. Prime factorization of 14008 in exponential form is:

14008 = 23 × 171 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 13996 and 14008.

LCM(13996,14008) = 23 × 34991 × 171 × 1031
LCM(13996,14008) = 49013992