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What is the Least Common Multiple of 65824 and 65840?

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 65824 and 65840 is 270865760.

LCM(65824,65840) = 270865760

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Least Common Multiple of 65824 and 65840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65824 and 65840, than apply into the LCM equation.

GCF(65824,65840) = 16
LCM(65824,65840) = ( 65824 × 65840) / 16
LCM(65824,65840) = 4333852160 / 16
LCM(65824,65840) = 270865760

Least Common Multiple (LCM) of 65824 and 65840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65824 and 65840. First we will calculate the prime factors of 65824 and 65840.

Prime Factorization of 65824

Prime factors of 65824 are 2, 11, 17. Prime factorization of 65824 in exponential form is:

65824 = 25 × 112 × 171

Prime Factorization of 65840

Prime factors of 65840 are 2, 5, 823. Prime factorization of 65840 in exponential form is:

65840 = 24 × 51 × 8231

Now multiplying the highest exponent prime factors to calculate the LCM of 65824 and 65840.

LCM(65824,65840) = 25 × 112 × 171 × 51 × 8231
LCM(65824,65840) = 270865760