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What is the Least Common Multiple of 65424 and 65440?

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 65424 and 65440 is 267584160.

LCM(65424,65440) = 267584160

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Least Common Multiple of 65424 and 65440 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65424 and 65440, than apply into the LCM equation.

GCF(65424,65440) = 16
LCM(65424,65440) = ( 65424 × 65440) / 16
LCM(65424,65440) = 4281346560 / 16
LCM(65424,65440) = 267584160

Least Common Multiple (LCM) of 65424 and 65440 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65424 and 65440. First we will calculate the prime factors of 65424 and 65440.

Prime Factorization of 65424

Prime factors of 65424 are 2, 3, 29, 47. Prime factorization of 65424 in exponential form is:

65424 = 24 × 31 × 291 × 471

Prime Factorization of 65440

Prime factors of 65440 are 2, 5, 409. Prime factorization of 65440 in exponential form is:

65440 = 25 × 51 × 4091

Now multiplying the highest exponent prime factors to calculate the LCM of 65424 and 65440.

LCM(65424,65440) = 25 × 31 × 291 × 471 × 51 × 4091
LCM(65424,65440) = 267584160