Question

the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively is

Answer 1

Firstly, we will find the LCM of the given numbers, i.e. , 20, 25, 35 and 40


20 => 2 × 5 × 2

25 => 5 × 5

35 => 7 × 5

40 => 2 × 5 × 2 × 2

LCM of 20, 25, 35 and 40 => 2 × 2 × 5 × 5 × 7 × 2 = 1400


When divided 20, 25, 35 and 40 by 14, 19, 29 and 34, i.e , 6 is less than the divisor.


So, we will subtract 6 from 1400

✒ 1400 - 6 = 1394




∴ The required number is $\bold{1394}$

Answer 2

$\huge \red{dear \: friend}$


here is your answer OK ☺☺☺☺☺☺☺


The smallest number which when divided by 20,25,35 and 40 leaves remainder of 14,19,29 and 34 respectively is ______

Here , we see

20-14 = 6

25 – 19 = 6

35-29 = 6

40-34 = 6

The difference is of 6

Now , taking LCM







5



20,25,35,40

5



4 , 5 , 7 , 8

2



4 , 1 , 7 , 8

2



2 , 1 , 7 , 4

2



1 , 1 , 7 , 2

7



1, 1, 7, 1





1 , 1, 1, 1



We get, 5* 5* 2*2*2*7 = 1400

So, the value will be 1400 – 6 = 1394 ans

Hence the answer is 1394