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What is the Least Common Multiple of 3978 and 3993?

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 3978 and 3993 is 5294718.

LCM(3978,3993) = 5294718

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Least Common Multiple of 3978 and 3993 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3978 and 3993, than apply into the LCM equation.

GCF(3978,3993) = 3
LCM(3978,3993) = ( 3978 × 3993) / 3
LCM(3978,3993) = 15884154 / 3
LCM(3978,3993) = 5294718

Least Common Multiple (LCM) of 3978 and 3993 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3978 and 3993. First we will calculate the prime factors of 3978 and 3993.

Prime Factorization of 3978

Prime factors of 3978 are 2, 3, 13, 17. Prime factorization of 3978 in exponential form is:

3978 = 21 × 32 × 131 × 171

Prime Factorization of 3993

Prime factors of 3993 are 3, 11. Prime factorization of 3993 in exponential form is:

3993 = 31 × 113

Now multiplying the highest exponent prime factors to calculate the LCM of 3978 and 3993.

LCM(3978,3993) = 21 × 32 × 131 × 171 × 113
LCM(3978,3993) = 5294718