Question

Find the smallest 4digit number
which when divided by 12, 15 , 18 will leave the
remainder as 8, 11 & 14 respectively? ​

Answer 1

We have to find LCM first

LCM of 12 , 15 , 18 is = 180 .

Now , multiply 180 with integer until it become a 4 digit number.

so ,

180× 1

180× 2

180× 3

.

.

.

180×6 = 1080 . ( we are doing this step because , 180 is divisible by 12, 15 & 18 , so 180×6 will also divisible)

since , they all will leave reminder of 4 .

substrates 4 from 1080

so the number is = 1080-4 = 1076

cross check :

1076÷12= 89 , rem= 8

1076÷15= 71 , rem = 11

1076÷ 18 =59 , rem =14

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