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What is the Least Common Multiple of 13948 and 13968?

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 13948 and 13968 is 48706416.

LCM(13948,13968) = 48706416

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Least Common Multiple of 13948 and 13968 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13948 and 13968, than apply into the LCM equation.

GCF(13948,13968) = 4
LCM(13948,13968) = ( 13948 × 13968) / 4
LCM(13948,13968) = 194825664 / 4
LCM(13948,13968) = 48706416

Least Common Multiple (LCM) of 13948 and 13968 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13948 and 13968. First we will calculate the prime factors of 13948 and 13968.

Prime Factorization of 13948

Prime factors of 13948 are 2, 11, 317. Prime factorization of 13948 in exponential form is:

13948 = 22 × 111 × 3171

Prime Factorization of 13968

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

13968 = 24 × 32 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 13948 and 13968.

LCM(13948,13968) = 24 × 111 × 3171 × 32 × 971
LCM(13948,13968) = 48706416