Question

Find the least number which when divided by 16,28,40 and 77 leaves 5 as a remainder in each case.

Answer 1

number = L.C.M ( 16 , 28 , 40 , 77) + 5
16 = 2 ^ 4
28 = 2 ² * 7
40 = 2³ * 5
77 = 11 * 7
∴lcm (16 , 28 , 40 , 77) = 2 ^ 4 *11 * 7 * 5 = 6160
therefore number = 6165

Answer 2

Answer:

The least number which when divided by 16,28,40 and 77 leaves 5 as a remainder in each case is 6165.

Step-by-step explanation:

To find : The least number which when divided by 16,28,40 and 77 leaves 5 as a remainder in each case?

Solution :

We find the LCM of 16,28,40 and 77.

2 | 16  28  40  77

2 | 8   14   20  77

2 | 4   7     10  77

2 | 2   7     5   77

5 | 1    7     5   77

7 | 1    7     1   77

11 | 1    1     1    11

   | 1    1     1     1

$LCM(16,28,40,77)=2\times 2\times 2\times 2\times 5\times 7\times 11$

$LCM(16,28,40,77)=6160$

In each case it leaves a remainder 5 so we add 5 in the LCM of the numbers.

i.e. 6160+5=6165.

Therefore, The least number which when divided by 16,28,40 and 77 leaves 5 as a remainder in each case is 6165.