Find the least number of five digits which when divided by...

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Find the least number of five digits which when divided by 40, 60, and 75, leave remainders 31, 51 and 66 respectively.

A. 10196

B. 10199

C. 10191

D. 10197

E. None of these

Answer: Option C

Solution(By Examveda Team)

Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75) - 9}

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
$$\frac{{10000}}{{600}},$$ we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191

This Question Belongs to Arithmetic Ability >> Number System

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Comments ( 3 )

X40 Gaming :

3 years ago

What is the least number of five digits which is divisible by 12 , 15 , 20 & 35 ?
Amit Singh :

4 years ago

Which is the greatest number of 5 digits which can be divided by 45, 60 & 70 leaves 20 as reminder on each cases
MITHUN SARKAR :

5 years ago

Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = (Least number of 5 digit) + {(LCM of 40, 60, 75)- (Least number of 5 digit)/ LCM} - difference between divider & remainder

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
10000/600, we get remainder as 400
Then, the answer = 10000 + (600 - 400) - 9 = 10191