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What is the Least Common Multiple of 3002 and 3006?

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 3002 and 3006 is 4512006.

LCM(3002,3006) = 4512006

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Least Common Multiple of 3002 and 3006 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3002 and 3006, than apply into the LCM equation.

GCF(3002,3006) = 2
LCM(3002,3006) = ( 3002 × 3006) / 2
LCM(3002,3006) = 9024012 / 2
LCM(3002,3006) = 4512006

Least Common Multiple (LCM) of 3002 and 3006 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3002 and 3006. First we will calculate the prime factors of 3002 and 3006.

Prime Factorization of 3002

Prime factors of 3002 are 2, 19, 79. Prime factorization of 3002 in exponential form is:

3002 = 21 × 191 × 791

Prime Factorization of 3006

Prime factors of 3006 are 2, 3, 167. Prime factorization of 3006 in exponential form is:

3006 = 21 × 32 × 1671

Now multiplying the highest exponent prime factors to calculate the LCM of 3002 and 3006.

LCM(3002,3006) = 21 × 191 × 791 × 32 × 1671
LCM(3002,3006) = 4512006