# Easy way to find the LCM of two numbers.

What is the Lowest Common Multiple (LCM) of 168 and 560?

- 1680
- 2240
- 1176
- 7840
- 2352

This question was given in Upper Primary category of the 3^{rd} International Vedic Mathematics Olympiad (IVMO 2023) and many contestants failed to get the correct answer.

The most common method taught in schools is to list down the multiples of each number and find out the smallest number which is found in both lists. But this would be cumbersome.

The Vedic method is to use the vertically and crosswise method. The initial steps of this method involves the procedure for finding the greatest common factor of the two numbers.

We can easily see that both 168 and 560 are divisible by 4, giving 42 and 140 respectively

Then 42 and 140 are both divisible by 14, resulting in quotients of 3 and 10.

Now 3 and 10 are relatively prime, that is, they have no common factor. We can now say that their greatest common factor is 4 x 14 or 56. But that is not required to solve this problem.

We only need to multiply one of the original numbers, 168, by 10 which is the result of dividing 560 successively by 4 and 14 to get 1680, the LCM of the two numbers. Note that we will also get 1680 if we multiply 560 by 3.