Find the $\mathrm{LCM}$ and $\mathrm{HCF}$ of $306$ and $657$ by the prime factorization method.

Write the terminating decimal $15.265$ in the form of $\frac{p}{q}, q\ne 0$ and $p, q$ are co-primes. Write the denominators in $2^n{5}^m$ form.

Write the terminating decimal $0.1255$ in the form of $\frac{p}{q}, q\ne 0$ and $p, q$ are co-primes. Write the denominators in $2^n{5}^m$ form.

Write the terminating decimal $0.4$ in the form of $\frac{p}{q}, q\ne 0$ and $p, q$ are co-primes. Write the denominators in $2^n{5}^m$ form.

Write the terminating decimal $23.34$ in the form of $\frac{p}{q}, q\ne 0$ and $p, q$ are co-primes. Write the denominators in $2^n{5}^m$ form.