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What is the Least Common Multiple of 82 and 102?

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 82 and 102 is 4182.

LCM(82,102) = 4182

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Least Common Multiple of 82 and 102 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82 and 102, than apply into the LCM equation.

GCF(82,102) = 2
LCM(82,102) = ( 82 × 102) / 2
LCM(82,102) = 8364 / 2
LCM(82,102) = 4182

Least Common Multiple (LCM) of 82 and 102 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82 and 102. First we will calculate the prime factors of 82 and 102.

Prime Factorization of 82

Prime factors of 82 are 2, 41. Prime factorization of 82 in exponential form is:

82 = 21 × 411

Prime Factorization of 102

Prime factors of 102 are 2, 3, 17. Prime factorization of 102 in exponential form is:

102 = 21 × 31 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 82 and 102.

LCM(82,102) = 21 × 411 × 31 × 171
LCM(82,102) = 4182

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