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

Contents

Problem based o LCM - AMC 8, 2016
- Key Concepts
Check the Answer
Try with Hints
Other useful links
Related Program
Subscribe to Cheenta at Youtube

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 $c$?

$26$
$20$
$28$

Key Concepts

Algebra

Divisor

multiplication

Check the Answer

But try the problem first...

Answer:20

Source

Try with Hints

First hint

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 ..........

Second Hint

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........

Final Step

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