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What is the Least Common Multiple of 3502 and 3514?

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 3502 and 3514 is 6153014.

LCM(3502,3514) = 6153014

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Least Common Multiple of 3502 and 3514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3502 and 3514, than apply into the LCM equation.

GCF(3502,3514) = 2
LCM(3502,3514) = ( 3502 × 3514) / 2
LCM(3502,3514) = 12306028 / 2
LCM(3502,3514) = 6153014

Least Common Multiple (LCM) of 3502 and 3514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3502 and 3514. First we will calculate the prime factors of 3502 and 3514.

Prime Factorization of 3502

Prime factors of 3502 are 2, 17, 103. Prime factorization of 3502 in exponential form is:

3502 = 21 × 171 × 1031

Prime Factorization of 3514

Prime factors of 3514 are 2, 7, 251. Prime factorization of 3514 in exponential form is:

3514 = 21 × 71 × 2511

Now multiplying the highest exponent prime factors to calculate the LCM of 3502 and 3514.

LCM(3502,3514) = 21 × 171 × 1031 × 71 × 2511
LCM(3502,3514) = 6153014