Try this beautiful problem from Algebra based on LCM from 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 $c$?
Algebra
Divisor
multiplication
But try the problem first...
Answer:20
AMC-8, 2016 problem 20
Challenges and Thrills of Pre College Mathematics
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
Try this beautiful problem from Algebra based on LCM from 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 $c$?
Algebra
Divisor
multiplication
But try the problem first...
Answer:20
AMC-8, 2016 problem 20
Challenges and Thrills of Pre College Mathematics
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