Question

Let x. be the least number which when
divided by 8, 12, 20, 28, 35 leaves a
remainder 5 in each case. What is the
sum of digits of x ?
(1) 11
(2) 14
(3) 15
(4) 17
​

Answer 1

Answer is 845

Step-by-step explanation:

LCM - Least Common Multiple for all the number is firstly calculated-  

LCM for each number is -

$8 = 2 \times 2 \times 2$

$12 = 2 \times 2 \times 3$

$20 = 2 \times 2 \times 5$

$28 = 2 \times 2 \times 7$

$35 = 5 \times 7$

Taking the Common factors, we get -

$LCM = 2 \times 2 \times 2 \times 3 \times 5 \times 7 = 840$

With the addition of 5 in the LCM we get the Answer as 845, as desired number.

Answer 2

(4) 17

The sum of digits of x is 17 .

Explanation:

Let x. be the least number which when  divided by 8, 12, 20, 28, 35 leaves a  remainder 5 in each case.

To find x , we first find LCM of 8, 12, 20, 28, 35.

Here , LCM = Least common multiple

8 = 2 x 2 x 2

12 = 2 x 2  x 3

20= 2 x 2  x 5

28 =2 x 2  x7

35 = 5 x 7

LCM of 8, 12, 20, 28, 35= $2\times2\times2\times3\times5\times7$

$=840$

As per given ,

x = LCM (8, 12, 20, 28, 35)+5

∴ x = 840+5 = 845

The sum of digits of x = 8+4+5=17

Hence, the correct answer is 4) 17 .

# Learn more :

Let x be a least number which when divided by 21, 33,35 and 55 leaves a remainder of 3. But is exactly divisible by 67

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