Dr Pooranmal and Ashfaq A Khan Solutions for Chapter: Factors and Multiples, Exercise 6: EXERCISE 4.6

When $35$ is added to a number, it is divisible by $5, 7, 9, 10$ and $15$. How many such numbers exist? Find the least of them?

When $28$ is subtracted from a number, the result is exactly divisible by $12, 15, 18$ and $36$. Find the least such number.

Find the smallest five-digit number which when divided by $16, 18, 24$ and $32$ leaves remainder $6$ in each case.

Find the greatest five-digit number which when divided by $12, 24, 30, 36$ and $45$ leaves remainder $8$ in each case.

Determine two numbers nearest to $10000$ which are exactly divisible by $8, 12, 15$ and $20$.

Find the least number which when divided by $12, 15, 18$ and $30$ leaves remainder $6, 9, 12$ and $24$ respectively.

The traffic lights at three different road-crossings change after every $48$ seconds, $72$ seconds and $108$ seconds respectively. They change simultaneously at $8$ am. After what time will they change again?

Three persons step off together for a morning walk. Their steps measure $72 \mathrm{cm}, 80 \mathrm{cm}$ and $84 \mathrm{cm}$ respectively. At what distance from the starting point will they again step off together?