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What is the Least Common Multiple of 6987 and 7002?

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 6987 and 7002 is 16307658.

LCM(6987,7002) = 16307658

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Least Common Multiple of 6987 and 7002 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6987 and 7002, than apply into the LCM equation.

GCF(6987,7002) = 3
LCM(6987,7002) = ( 6987 × 7002) / 3
LCM(6987,7002) = 48922974 / 3
LCM(6987,7002) = 16307658

Least Common Multiple (LCM) of 6987 and 7002 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6987 and 7002. First we will calculate the prime factors of 6987 and 7002.

Prime Factorization of 6987

Prime factors of 6987 are 3, 17, 137. Prime factorization of 6987 in exponential form is:

6987 = 31 × 171 × 1371

Prime Factorization of 7002

Prime factors of 7002 are 2, 3, 389. Prime factorization of 7002 in exponential form is:

7002 = 21 × 32 × 3891

Now multiplying the highest exponent prime factors to calculate the LCM of 6987 and 7002.

LCM(6987,7002) = 32 × 171 × 1371 × 21 × 3891
LCM(6987,7002) = 16307658