Find the LCM of 3 numbers given HCF of each 2. 
Answer is 
I was totally confused when I saw the question. I never encountered a question like this.
Can anyone tell me the way to solve this.
I tried every method I could find but hard luck.

Hint: Proceed one prime at a time. Let's deal with $2$.
The highest power of $2$ that divides $a$ and $b$ is $2^3$.
But the highest power of $2$ that divides $b$ is at least $2^4$, since $\gcd(b,c)$ is divisible by $2^4$.
So the highest power of $2$ that divides $a$ is $2^3$.
Since $2^4$ divides both $b$ and $c$, it follows that $abc$ is divisible by $2^{3+4+4}=2^{11}$.
But the highest power of $2$ that divides $abc$ is $2^{11}$.
So the highest power of $2$ that divides $b$ is $2^4$, and the same is true of $c$.
So the powers are $2^3$, $2^4$, $2^4$, which means that the exponent of $2$ in the LCM is $\max(3,4,4)$, which is $4$.
Continue, reasoning your way with $3$, with $5$, with $7$.
