If two positive integers $a$ and $b$ are written as $a = x^3 y^2$ and $b = x y^3$,where $x$ and $y$ are prime numbers,then $HCF(a, b)$ is:

The Least Common Multiple $(LCM)$ of two distinct prime numbers $a$ and $b$ is:

There is a circular path around a sports field. Sonia takes $18$ minutes to drive one round of the field,while Ravi takes $12$ minutes for the same. Suppose they both start at the same point and at the same time,and go in the same direction. After how many minutes will they meet again at the starting point?

Find the largest number which divides $615$ and $963$ leaving remainder $6$ in each case.

The largest number which divides $70$ and $125,$ leaving remainders $5$ and $8$ respectively,is

If $HCF(a, b) = 12$, then which of the following cannot be the $LCM(a, b)$?