Question

find the least number that will divided by 9,11,13 gives remainder 1,2,3.​

Answer 1

Answer:

Answer is 360 first subtract 1from 9,2from 11 ,and 3 from 13 then find LCM of 8,9,10

Answer 2

Answer:

we have to find least number which is divisible by 9,11 , 13 and also leaves remainder 1,2,3 ...

Now, your solution

let the smallest no be x

x / 9 = 1 remainder

x / 11 = 2 remainder

x / 13 = 3 remainder

both side multiply by 2

2x / 9 = remainder 2

2x / 11 = remainder 4

2x / 13 = remainder 6

now you noticed that if we add 7 to 2x so all numbers are fully divisible.

2x + 7/9 = 0 ( remainder)

2x + 7 / 11 = 0 ( remainder)

2x + 7/ 13 = 0 ( remainder)

this shows that 2x + 7 is completely divisible by 9 , 11 , 13

now multiply 9 * 11 * 13 = 1287

2x + 7 = 1287

2x = 1287 - 7 = 1280

x = 1280 / 2= 640

so 640 is the least number which is divisible by 9,11,13 and leaves remainder 1, 2, 3

I hope my answer is helpful for you ✌✌