By using the fact $g.c.d. (a, b) \times l.c.m. (a, b) = a \times b$,find $l.c.m. (26, 91)$.

Prove that one of any three consecutive positive integers must be divisible by $3$.

Prove that $\sqrt{3}$ is an irrational number.

$A$ positive integer is of the form $3q + 1$,where $q$ is a natural number. Can you write its square in any form other than $3m + 1$,i.e.,$3m$ or $3m + 2$ for some integer $m$? Justify your answer.

Express $156$ as a product of primes.

The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $3.127$