# How to find the LCM of One Negative and one positive Integer

The title pretty much explains my question. While studying theory of numbers I came across this problem. The way I did LCM in childhood gave me a negative result.Maybe the method I used is wrong.

But according to the book, LCM(-8,20)= 40

If I use the formula LCM(a,b)= |a.b|/GCD(a,b), Then I get the right answer. But this involves finding out gcd first. Is there a direct way to solve this problem?

Thank you in advance.

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The lowest common multiple of $[a,b]$ is the least positive integer such that both numbers divide into. And any other multiple of those two numbers, the lcm divides into as well. –  user60887 Oct 27 '13 at 16:41

An alternative to using the $\operatorname{lcm}(a,b)=\frac{|a\cdot b|}{\gcd(a,b)}$ relationship, is to break the absolute value of the numbers into their prime factors, and then multiply the highest powers of each prime (lcm by prime factorization).
For example, $|-8|=2^3$, and $|20|=2^2\cdot 5$, and so $\operatorname{lcm}(-8,20)=2^3\cdot5$.
Note : The LCM is defined as the least common multiple of the numbers that is positive. Or else, the answer would be $- \infty$. This explains it.