The least number that is divisible by all the numbers from $1$ to $10$ (both inclusive) is

There is a circular path around a sports field. Kushan takes $18$ minutes to complete one round of the field,while Rajan 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?

The following real number is expressed in decimal form: $0.05005000500005 \ldots$. Determine whether it is rational or irrational. If it is rational,express it in the form of $\frac{p}{q}$.

Why are the following numbers composite? Explain: $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$

$A$ rational number in its decimal expansion is $327.7081$. What can you say about the prime factors of $q$,when this number is expressed in the form $\frac{p}{q}$? Give reasons.

The value obtained after rationalising the denominator of $\frac{1}{3+\sqrt{8}}$ is $\ldots \ldots$