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What is the Least Common Multiple of 1730 and 1738?

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 1730 and 1738 is 1503370.

LCM(1730,1738) = 1503370

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Least Common Multiple of 1730 and 1738 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1730 and 1738, than apply into the LCM equation.

GCF(1730,1738) = 2
LCM(1730,1738) = ( 1730 × 1738) / 2
LCM(1730,1738) = 3006740 / 2
LCM(1730,1738) = 1503370

Least Common Multiple (LCM) of 1730 and 1738 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1730 and 1738. First we will calculate the prime factors of 1730 and 1738.

Prime Factorization of 1730

Prime factors of 1730 are 2, 5, 173. Prime factorization of 1730 in exponential form is:

1730 = 21 × 51 × 1731

Prime Factorization of 1738

Prime factors of 1738 are 2, 11, 79. Prime factorization of 1738 in exponential form is:

1738 = 21 × 111 × 791

Now multiplying the highest exponent prime factors to calculate the LCM of 1730 and 1738.

LCM(1730,1738) = 21 × 51 × 1731 × 111 × 791
LCM(1730,1738) = 1503370