User:AnmolSrivastava274/sandbox

I've included the image on the right to demonstrate a key component of the nature of co-prime integers. This component is described in one short line on the Wikipedia age for the same topic. In essence, it denotes that if two numbers are co-prime, then their lowest common multiple (LCM) is their product. A thorough understanding of relatively prime numbers may make this fact clearer - if two numbers share no common factor other than 1, then their multiples will not also be multiples of any other number - and their common multiple can come no sooner than when one is multiplied by the other.

But if a first-time reader views the page's short statement on the matter, or prefers learning from a visual supplement, they may be confused. This picture (my original work) uses 3 and 5 as examples. These numbers are co-prime and have LCM 15 (their product). The image visually demonstrates how the two numbers' multiples lead to the first common one (15). It shows that since there is no shared denominator among the numbers, the multiples only increase by 3 or 5 themselves. As a counterexample, take 2 and 4. Now, 4's multiples increase in multiples of 4, but also in multiples of 2, which is common to 2 (the other number). Returning to the 3-5 example, the earliest common multiple can hence only be when 3 is multiplied by 5 and 5 by 3.

This simple, comparative line-drawing can (in my view) really elucidate a simple fact, which may not be immediately intuitive. I anticipate that adding this drawing to the Wiki can help more casual viewers process the more important parts of the page (ignoring the specific applications and theoretical concepts), and understand the true principles and properties of co-prime numbers in a better way.