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What is the Least Common Multiple of 8414 and 8420?

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 8414 and 8420 is 35422940.

LCM(8414,8420) = 35422940

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Least Common Multiple of 8414 and 8420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8414 and 8420, than apply into the LCM equation.

GCF(8414,8420) = 2
LCM(8414,8420) = ( 8414 × 8420) / 2
LCM(8414,8420) = 70845880 / 2
LCM(8414,8420) = 35422940

Least Common Multiple (LCM) of 8414 and 8420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8414 and 8420. First we will calculate the prime factors of 8414 and 8420.

Prime Factorization of 8414

Prime factors of 8414 are 2, 7, 601. Prime factorization of 8414 in exponential form is:

8414 = 21 × 71 × 6011

Prime Factorization of 8420

Prime factors of 8420 are 2, 5, 421. Prime factorization of 8420 in exponential form is:

8420 = 22 × 51 × 4211

Now multiplying the highest exponent prime factors to calculate the LCM of 8414 and 8420.

LCM(8414,8420) = 22 × 71 × 6011 × 51 × 4211
LCM(8414,8420) = 35422940