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# Problem based on LCM | AMC 8, 2016 | Problem 20

Try this beautiful problem from Algebra based on LCM from AMC-8, 2016. You may use sequential hints to solve the problem.

Try this beautiful problem from Algebra based on LCM from AMC-8, 2016.

## Problem based on LCM – AMC 8, 2016

The least common multiple of $a$ and $b$ is $12$, and the least common multiple of $b$ and $c$ is $15$. What is the least possible value of the least common multiple of $a$ and $c$?

• $26$
• $20$
• $28$

Algebra

Divisor

multiplication

## Check the Answer

AMC-8, 2016 problem 20

Challenges and Thrills of Pre College Mathematics

## Try with Hints

We have to find out the least common multiple of $a$ and $c$.if you know the value of $a$ and $c$ then you can easily find out the required LCM. Can you find out the value of $a$ and $c$?

Can you now finish the problem ……….

Given that the least common multiple of $a$ and $b$ is $12$, and the least common multiple of $b$ and $c$ is $15$ .then b must divide 12 and 15. There is only one possibility that b=3 which divide 12 and 15. therefore $a$=$\frac{12}{3}=4$

can you finish the problem……..

so$b$=3. Given that LCM of $b$ and $c$ is 15. Therefore c=5

Now lcm of $a$ and $c$ that is lcm of 4 and 5=20