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What is the Least Common Multiple of 7990 and 8002?

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 7990 and 8002 is 31967990.

LCM(7990,8002) = 31967990

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Least Common Multiple of 7990 and 8002 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7990 and 8002, than apply into the LCM equation.

GCF(7990,8002) = 2
LCM(7990,8002) = ( 7990 × 8002) / 2
LCM(7990,8002) = 63935980 / 2
LCM(7990,8002) = 31967990

Least Common Multiple (LCM) of 7990 and 8002 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7990 and 8002. First we will calculate the prime factors of 7990 and 8002.

Prime Factorization of 7990

Prime factors of 7990 are 2, 5, 17, 47. Prime factorization of 7990 in exponential form is:

7990 = 21 × 51 × 171 × 471

Prime Factorization of 8002

Prime factors of 8002 are 2, 4001. Prime factorization of 8002 in exponential form is:

8002 = 21 × 40011

Now multiplying the highest exponent prime factors to calculate the LCM of 7990 and 8002.

LCM(7990,8002) = 21 × 51 × 171 × 471 × 40011
LCM(7990,8002) = 31967990