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What is the Least Common Multiple of 13978 and 13985?

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 13978 and 13985 is 195482330.

LCM(13978,13985) = 195482330

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Least Common Multiple of 13978 and 13985 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13978 and 13985, than apply into the LCM equation.

GCF(13978,13985) = 1
LCM(13978,13985) = ( 13978 × 13985) / 1
LCM(13978,13985) = 195482330 / 1
LCM(13978,13985) = 195482330

Least Common Multiple (LCM) of 13978 and 13985 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13978 and 13985. First we will calculate the prime factors of 13978 and 13985.

Prime Factorization of 13978

Prime factors of 13978 are 2, 29, 241. Prime factorization of 13978 in exponential form is:

13978 = 21 × 291 × 2411

Prime Factorization of 13985

Prime factors of 13985 are 5, 2797. Prime factorization of 13985 in exponential form is:

13985 = 51 × 27971

Now multiplying the highest exponent prime factors to calculate the LCM of 13978 and 13985.

LCM(13978,13985) = 21 × 291 × 2411 × 51 × 27971
LCM(13978,13985) = 195482330