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What is the Least Common Multiple of 3968 and 3975?

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 3968 and 3975 is 15772800.

LCM(3968,3975) = 15772800

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Least Common Multiple of 3968 and 3975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3968 and 3975, than apply into the LCM equation.

GCF(3968,3975) = 1
LCM(3968,3975) = ( 3968 × 3975) / 1
LCM(3968,3975) = 15772800 / 1
LCM(3968,3975) = 15772800

Least Common Multiple (LCM) of 3968 and 3975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3968 and 3975. First we will calculate the prime factors of 3968 and 3975.

Prime Factorization of 3968

Prime factors of 3968 are 2, 31. Prime factorization of 3968 in exponential form is:

3968 = 27 × 311

Prime Factorization of 3975

Prime factors of 3975 are 3, 5, 53. Prime factorization of 3975 in exponential form is:

3975 = 31 × 52 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 3968 and 3975.

LCM(3968,3975) = 27 × 311 × 31 × 52 × 531
LCM(3968,3975) = 15772800