Express $140$ as a product of its prime factors.

Find the $LCM$ and $HCF$ of the following pairs of integers and verify that $LCM \times HCF =$ product of the two numbers $336$ and $54$.

Prove that $6+\sqrt{2}$ is an irrational number.

Prove that $7 \sqrt{5}$ is an irrational number.

Determine whether the rational number $\frac{77}{210}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

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?