The product of two numbers is $6760$ and their $H.C.F.$ is $13.$ How many such pairs can be formed?

The least multiple of $7,$ which leaves a remainder of $4,$ when divided by $6, 9, 15,$ and $18$ is

$A$ heap of stones can be made up into groups of $21$. When made up into groups of $16, 20, 25$ and $45$,there are $3$ stones left in each case. How many stones at least can there be in the heap?

Five bells begin to toll together and toll at intervals of $36, 45, 72, 81$ and $108$ seconds. After what interval of time will they keep on tolling together? (in $seconds$)

The $LCM$ of $2^{2} \times 3^{2} \times 5 \times 11$,$2^{4} \times 3^{4} \times 5^{2} \times 7$,and $2^{5} \times 3^{3} \times 5^{2} \times 7^{2} \times 11$ is:

How often will five bells toll together in one hour if they start together and toll at intervals of $5, 6, 8, 12, 20$ seconds,respectively?