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What is the Least Common Multiple of 13968 and 13975?

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 13968 and 13975 is 195202800.

LCM(13968,13975) = 195202800

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Least Common Multiple of 13968 and 13975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13968 and 13975, than apply into the LCM equation.

GCF(13968,13975) = 1
LCM(13968,13975) = ( 13968 × 13975) / 1
LCM(13968,13975) = 195202800 / 1
LCM(13968,13975) = 195202800

Least Common Multiple (LCM) of 13968 and 13975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13968 and 13975. First we will calculate the prime factors of 13968 and 13975.

Prime Factorization of 13968

Prime factors of 13968 are 2, 3, 97. Prime factorization of 13968 in exponential form is:

13968 = 24 × 32 × 971

Prime Factorization of 13975

Prime factors of 13975 are 5, 13, 43. Prime factorization of 13975 in exponential form is:

13975 = 52 × 131 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 13968 and 13975.

LCM(13968,13975) = 24 × 32 × 971 × 52 × 131 × 431
LCM(13968,13975) = 195202800