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What is the Least Common Multiple of 13960 and 13971?

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 13960 and 13971 is 195035160.

LCM(13960,13971) = 195035160

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Least Common Multiple of 13960 and 13971 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13960 and 13971, than apply into the LCM equation.

GCF(13960,13971) = 1
LCM(13960,13971) = ( 13960 × 13971) / 1
LCM(13960,13971) = 195035160 / 1
LCM(13960,13971) = 195035160

Least Common Multiple (LCM) of 13960 and 13971 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13960 and 13971. First we will calculate the prime factors of 13960 and 13971.

Prime Factorization of 13960

Prime factors of 13960 are 2, 5, 349. Prime factorization of 13960 in exponential form is:

13960 = 23 × 51 × 3491

Prime Factorization of 13971

Prime factors of 13971 are 3, 4657. Prime factorization of 13971 in exponential form is:

13971 = 31 × 46571

Now multiplying the highest exponent prime factors to calculate the LCM of 13960 and 13971.

LCM(13960,13971) = 23 × 51 × 3491 × 31 × 46571
LCM(13960,13971) = 195035160