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What is the Least Common Multiple of 1715 and 1734?

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 1715 and 1734 is 2973810.

LCM(1715,1734) = 2973810

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Least Common Multiple of 1715 and 1734 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1715 and 1734, than apply into the LCM equation.

GCF(1715,1734) = 1
LCM(1715,1734) = ( 1715 × 1734) / 1
LCM(1715,1734) = 2973810 / 1
LCM(1715,1734) = 2973810

Least Common Multiple (LCM) of 1715 and 1734 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1715 and 1734. First we will calculate the prime factors of 1715 and 1734.

Prime Factorization of 1715

Prime factors of 1715 are 5, 7. Prime factorization of 1715 in exponential form is:

1715 = 51 × 73

Prime Factorization of 1734

Prime factors of 1734 are 2, 3, 17. Prime factorization of 1734 in exponential form is:

1734 = 21 × 31 × 172

Now multiplying the highest exponent prime factors to calculate the LCM of 1715 and 1734.

LCM(1715,1734) = 51 × 73 × 21 × 31 × 172
LCM(1715,1734) = 2973810