What is the Logic of LCM for java programs?

Answer 1

Factoring numbers into prime numbers, as taught in school, is much too complicated to program. To write a simple computer program, I would use the formula:

a x b = lcm(a, b) x gcd(a, d)

In other words, lcm(a, b) = a x b / gcf(a, d).

The greatest common factor can be found easily with Euclid's Formula. For example, to calculate the greatest common factor of 14 and 10:

gcf(14, 10) is the same as gcf(10, 4), where 4 is calculated as 14 % 10.

gcf(10, 4) is the same as gcf(4, 2). Again, 2 is calculated as 10 % 4.

Once you get a remainder of zero, stop. In this case, 4 % 2 = 0, so 2 is the gcf. In this case, the lcm can be calculated as 14 * 10 / 2.

Answer 2

private int calculateLCM(int input[]) {

int LCM = input[0], tempCount = 0,tempVal = 0,num = 0;

try {

for (int i = 1; i < input.length; i++) {

LCM = Math.max(LCM, input[i]);

num = Math.min(LCM, input[i]);

tempVal = LCM;

tempCount = 2;

while ((tempVal % num) != 0) {

tempVal = LCM * tempCount;

tempCount++;

}

LCM = tempVal;

}

} catch (Exception e) {

e.printStackTrace();

}

return LCM;

}