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What is the Least Common Multiple of 3965 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 3965 and 3975 is 3152175.

LCM(3965,3975) = 3152175

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Least Common Multiple of 3965 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 3965 and 3975, than apply into the LCM equation.

GCF(3965,3975) = 5
LCM(3965,3975) = ( 3965 × 3975) / 5
LCM(3965,3975) = 15760875 / 5
LCM(3965,3975) = 3152175

Least Common Multiple (LCM) of 3965 and 3975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3965 and 3975. First we will calculate the prime factors of 3965 and 3975.

Prime Factorization of 3965

Prime factors of 3965 are 5, 13, 61. Prime factorization of 3965 in exponential form is:

3965 = 51 × 131 × 611

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 3965 and 3975.

LCM(3965,3975) = 52 × 131 × 611 × 31 × 531
LCM(3965,3975) = 3152175