Question

Question 197

In a colony of 100 blocks of flats numbered from 1 to 100, a school van stops at every sixth block, while a school bus stops at every tenth block. On which stops will both of them stop, if they start from the entrance of the colony?

Answer 1

Given, in a colony of 100 blocks, there are 100 flats numbering from 1 to 100.

Here, school van and bus stop at the same stoppage means it is the LCM of both stoppages.

Now, LCM of 6 and 10

$\begin{array}{ccc}& 2& 6,10\\ & 3& 3,5\\ & 5& 1,5\\ & & 1,1\end{array}$

LCM of 6 and 10 $=2\times 3\times 5=30$

It shows that first time they both meets at 30th stoppage and the next time they again meet at a multiple of 30.
Multiples of 30, which are less than 100, are 30, 60 and 90.
Hence, both will stop at the stop blocks 30th, 60th and 90th, if they start from the entrance of the colony.