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What is the Least Common Multiple of 8214 and 8218?

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 8214 and 8218 is 33751326.

LCM(8214,8218) = 33751326

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Least Common Multiple of 8214 and 8218 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8214 and 8218, than apply into the LCM equation.

GCF(8214,8218) = 2
LCM(8214,8218) = ( 8214 × 8218) / 2
LCM(8214,8218) = 67502652 / 2
LCM(8214,8218) = 33751326

Least Common Multiple (LCM) of 8214 and 8218 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8214 and 8218. First we will calculate the prime factors of 8214 and 8218.

Prime Factorization of 8214

Prime factors of 8214 are 2, 3, 37. Prime factorization of 8214 in exponential form is:

8214 = 21 × 31 × 372

Prime Factorization of 8218

Prime factors of 8218 are 2, 7, 587. Prime factorization of 8218 in exponential form is:

8218 = 21 × 71 × 5871

Now multiplying the highest exponent prime factors to calculate the LCM of 8214 and 8218.

LCM(8214,8218) = 21 × 31 × 372 × 71 × 5871
LCM(8214,8218) = 33751326