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

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

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{23}{2^{3} \times 5^{2}}$

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{13}{3125}$.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{6}{15}$

Find the $HCF$ of $96$ and $404$ by the prime factorisation method. Hence,find their $LCM$.