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What is the Least Common Multiple of 13971 and 13980?

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 13971 and 13980 is 65104860.

LCM(13971,13980) = 65104860

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Least Common Multiple of 13971 and 13980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13971 and 13980, than apply into the LCM equation.

GCF(13971,13980) = 3
LCM(13971,13980) = ( 13971 × 13980) / 3
LCM(13971,13980) = 195314580 / 3
LCM(13971,13980) = 65104860

Least Common Multiple (LCM) of 13971 and 13980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13971 and 13980. First we will calculate the prime factors of 13971 and 13980.

Prime Factorization of 13971

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

13971 = 31 × 46571

Prime Factorization of 13980

Prime factors of 13980 are 2, 3, 5, 233. Prime factorization of 13980 in exponential form is:

13980 = 22 × 31 × 51 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 13971 and 13980.

LCM(13971,13980) = 31 × 46571 × 22 × 51 × 2331
LCM(13971,13980) = 65104860