Question

24. The least number which when divided by
24, 32 and 36 leaves the remainders 19, 27
and 31 respectively, is
(b) 140
(d) 283
(a) 360
(c) 280​

Answer 1

Answer:

First, we need to find the LCM of 24, 36 and 48. The LCM of 24, 36 and 48 is 144.

Now, we shall find the difference of 24 and 21 which is 3. Similarly, the difference of 36 and 33 and also that of 48 and 45 is 3 respectively.

The difference between the LCM and 3 is the smallest number.

So, 144 - 3 = 141.

Hence, 141 is the smallest number when divided by 24, 36 and 48 leave remainders 21, 33 and 45 respectively.