Question

What least possible 4 digit number when divided by 12, 16, 18 and 20 leaves the remainder 21?

Answer 1

i think so it is 1962

Answer 2

Answer:

Required Number is 1461.

Step-by-step explanation:

Given Numbers are 12 , 16 , 18 and 20.

We have to find 4-digit least number divisible by given number such that leaves 21 as remainder every time.

We first Find LCM of given numbers.

12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2

18 = 2 × 3 × 3

20 = 2 × 2 × 5

LCM ( 12 , 16 , 18 , 20 ) = 2 × 2 × 3 × 2 × 2 × 3 × 5 = 720

Now to find least 4-digit number we find multiple of 720.

720 , 1440 , 2160 , 2880 , 3600 ...

So, 1440 is the least 4-digit number divisible by 12 , 16 , 18 , 20

Now we need to find number which leaves 21 as remainder.

So, we add 21 to 1440 = 1440 + 21 = 1461

Therefore, Required Number is 1461.