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What is the Least Common Multiple of 345 and 362?

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 345 and 362 is 124890.

LCM(345,362) = 124890

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Least Common Multiple of 345 and 362 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 362, than apply into the LCM equation.

GCF(345,362) = 1
LCM(345,362) = ( 345 × 362) / 1
LCM(345,362) = 124890 / 1
LCM(345,362) = 124890

Least Common Multiple (LCM) of 345 and 362 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 362. First we will calculate the prime factors of 345 and 362.

Prime Factorization of 345

Prime factors of 345 are 3, 5, 23. Prime factorization of 345 in exponential form is:

345 = 31 × 51 × 231

Prime Factorization of 362

Prime factors of 362 are 2, 181. Prime factorization of 362 in exponential form is:

362 = 21 × 1811

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 362.

LCM(345,362) = 31 × 51 × 231 × 21 × 1811
LCM(345,362) = 124890