## LCM – AMC 8, 2016 – Problem 20

The least common multiple of a and b is 12 .and the lest common multiple of b and c is 15.what is the least possible value of the least common multiple of a and c?

- 30
- 60
- 20

**Key Concepts**

Algebra

Division algorithm

Integer

## Check the Answer

But try the problem first…

Answer:20

AMC-8, 2016 problem 20

Challenges and Thrills of Pre College Mathematics

## Try with Hints

First hint

Find greatest common factors

Can you now finish the problem ……….

Second Hint

Find Least common multiple….

can you finish the problem……..

Final Step

we wish to find possible values of a,b and c .By finding the greatest common factor 12 and 15, algebrically ,it’s some multiple of b and from looking at the numbers ,we are sure that it is 3.Moving on to a and c ,in order to minimize them,we wish to find the least such that the LCM of a and 3 is 12,$\to 4$.similarly with 3 and c,we obtain 5.the LCM of 4 and 5 is 20 .

## Other useful links

- https://www.cheenta.com/area-of-a-triangle-amc-8-2018-problem-20/
- https://www.youtube.com/watch?v=mEqBRtplXck