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What is the Least Common Multiple of 3008 and 3014?

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 3008 and 3014 is 4533056.

LCM(3008,3014) = 4533056

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Least Common Multiple of 3008 and 3014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3008 and 3014, than apply into the LCM equation.

GCF(3008,3014) = 2
LCM(3008,3014) = ( 3008 × 3014) / 2
LCM(3008,3014) = 9066112 / 2
LCM(3008,3014) = 4533056

Least Common Multiple (LCM) of 3008 and 3014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3008 and 3014. First we will calculate the prime factors of 3008 and 3014.

Prime Factorization of 3008

Prime factors of 3008 are 2, 47. Prime factorization of 3008 in exponential form is:

3008 = 26 × 471

Prime Factorization of 3014

Prime factors of 3014 are 2, 11, 137. Prime factorization of 3014 in exponential form is:

3014 = 21 × 111 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 3008 and 3014.

LCM(3008,3014) = 26 × 471 × 111 × 1371
LCM(3008,3014) = 4533056