Jayashri Bhattacharya and Tarika Dhawan Solutions for Exercise 6: Unit Innings

Write the smallest $6‐$digit number and its predecessor.

I am a number between a pair of twin primes. I am a multiple of $2,3,4,5,6$. What number am I?

Find the smallest number that should be added to $4135$ so that it is exactly divisible by $37$.

Write the smallest $4‐$digit number that is divisible by $3$ and $9$.

Find the smallest number that when divided by $14,$ $28,$ $91$ leaves a remainder $1$ in each case.

The product of two co-prime numbers is $117$. Find their LCM.

A courtyard is $6$ $\mathrm{m}$ long and $5$ $\mathrm{m}$ wide. Arhan covers the courtyard with square tiles without cutting them. The largest size of each tile used by Arhan is $1 {\mathrm{m}}^2$. Find the number of tiles required?

Three ropes of lengths $6$ $\mathrm{m}$ $30$ $\mathrm{cm}$, $5$ $\mathrm{m}$ $85$ $\mathrm{cm}$ and $3$ $\mathrm{m}$ $60$ $\mathrm{cm}$, respectively, are cut into smaller pieces of equal length. What will be the greatest possible length of each piece?