Question

The smallest number which when divided by 24, 32 and 36 leaves reminders as 19,27 and 31 respectively is

Answer 1

Let the smallest number be equal to x .

First we will find the LCM of the numbers 24, 32 and 36.

The LCM of the three numbers will come out be equal to 288.

The difference between the remainder and the divisor is -

24-19 = 5

32-27 = 5

36-31 = 5

The difference in each case is each case comes out be equal to 5.

x= LCM - difference

x= 288 - 5

x= 283

The smallest number is equal to 288.