LCM – Interesting Smallest Number Puzzle

Lcm Puzzle

I guess you might have used the concept of LCM ( Least Common Multiples ) many times in a grocery store while purchasing stuff without even realizing it. Remember the time when you had to pair up items and their package sizes were different and you didn’t want any “wastage”. How did you figure out how many of each item to buy ? For example, if the sausages are sold in a pack of 8 and buns in a pack of 12, how many of each you should buy so that there is no surplus. You used the concept of LCM and bought 3 packs of sausages and 2 packs of bun. This Interesting smallest number puzzle comes with a twist but can also be solved using the concept of LCM. Can you figure it out ?


The Smallest Number Puzzle

Can you figure out the smallest number with the following properties

Give the problem a try and leave your answers in the comments section or click below for the solution.

As you can see, using the concept of LCM we were easily able to solve this interesting smallest number puzzle.


LCM stands for least common multiple. The LCM of two or more numbers is the smallest number which is a multiple of all of the numbers.

So, how in real life it can used. Looking at the same example in the beginning, let’s say you are at the grocery store to buy sausages and buns for a party you’re hosting. You find that the sausages are sold in a pack of 8 and buns in a pack of 12. What is the least number of sausages and buns you need to buy in order to make sure there is an equal number of buns of sausages and nothing is leftover.

The answer would be the LCM(8, 12) = 24. The prime factors of 12 are 2 x 2 x 3. The prime factors of 8 are 2 x 2 x 2. Therefore, common factor of 12 and 8 are 2 x 2 x 2 x 3 =24.

So, you need to buy

  • 3 packs of sausages ( 8 x 3 = 24 ) and
  • 2 ( 12 x 2 ) packs of buns.

If you are like me and love math and puzzles then check out my 30+ list of math puzzles and brainteasers.

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