In a school,$391$ boys and $323$ girls have been divided into the largest possible equal classes,so that each class of boys numbers the same as each class of girls. What is the number of classes?

Find the sum of the numbers between $500$ and $700$ such that when they are divided by $6, 8$ and $12$ it leaves no remainder.

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?

Three men start together to travel the same way around a circular track of $11 \text{ km}$ in circumference. Their speeds are $4 \text{ km/h}$,$5.5 \text{ km/h}$,and $8 \text{ km/h}$ respectively. When will they meet at the starting point? (in hours)

What is the least number of cut pieces of equal length that can be cut out of two lengths $10\, m\, 857\, mm$ and $15\, m\, 87\, mm$?

$A$ room is $4\, m\, 37\, cm$ long and $3\, m\, 23\, cm$ broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for this purpose.