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What is the Least Common Multiple of 39 and 59?

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 39 and 59 is 2301.

LCM(39,59) = 2301

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Least Common Multiple of 39 and 59 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39 and 59, than apply into the LCM equation.

GCF(39,59) = 1
LCM(39,59) = ( 39 × 59) / 1
LCM(39,59) = 2301 / 1
LCM(39,59) = 2301

Least Common Multiple (LCM) of 39 and 59 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39 and 59. First we will calculate the prime factors of 39 and 59.

Prime Factorization of 39

Prime factors of 39 are 3, 13. Prime factorization of 39 in exponential form is:

39 = 31 × 131

Prime Factorization of 59

Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:

59 = 591

Now multiplying the highest exponent prime factors to calculate the LCM of 39 and 59.

LCM(39,59) = 31 × 131 × 591
LCM(39,59) = 2301

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