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What is the Least Common Multiple of 65742 and 65760?

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 65742 and 65760 is 720532320.

LCM(65742,65760) = 720532320

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Least Common Multiple of 65742 and 65760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65742 and 65760, than apply into the LCM equation.

GCF(65742,65760) = 6
LCM(65742,65760) = ( 65742 × 65760) / 6
LCM(65742,65760) = 4323193920 / 6
LCM(65742,65760) = 720532320

Least Common Multiple (LCM) of 65742 and 65760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65742 and 65760. First we will calculate the prime factors of 65742 and 65760.

Prime Factorization of 65742

Prime factors of 65742 are 2, 3, 10957. Prime factorization of 65742 in exponential form is:

65742 = 21 × 31 × 109571

Prime Factorization of 65760

Prime factors of 65760 are 2, 3, 5, 137. Prime factorization of 65760 in exponential form is:

65760 = 25 × 31 × 51 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 65742 and 65760.

LCM(65742,65760) = 25 × 31 × 109571 × 51 × 1371
LCM(65742,65760) = 720532320