Question

What is the least number that must be subtracted by 3000 so that the difference is divisible exactly by 33, 32 and 48 ?

Answer 1

Hello Dear.

Here is your answer---

Let the number that must be Subtracted from 3000 be x.

Taking an L.C.M. of 33,32 and 48.
∴ L.C.M. is 1056.

Now,
  3000 - x will be the smallest number which will be divisible by the 1056

∴ 3000 - x = 1056
 ⇒ x = 3000 - 1056
 ⇒ x = 1944

Thus, the Least number which must be subtracted from by 3000 so that the difference is divisible by 33,32 and 48  is 1944.


Hope it helps.

Answer 2

Solution :-

Let the required number which must be subtracted from 3000 be 'x'

We have to find the LCM of 33, 32 and 48

33 = 3*11

32 = 2*2*2*2*2

48 = 2*2*2*2*3

LCM of 33, 32 and 48 = 2*2*2*2*2*3*11

= 1056

So, LCM of 33, 32 and 48 is 1056

Now,

We will subtract maximum possible multiple of 1056 (LCM of 33, 32 and 48) from 3000.

⇒ x = 3000 - (2*1056)

⇒ x = 3000 - 2112

⇒ x = 888

So, 888 is the least number which must be subtracted from 3000 so that the difference is exactly divisible by 33, 32 and 48.

_____________________________________________________________

Let us check our answer.

3000 - 888 = 2112

2112 ÷ 33 

Quotient = 64, Remainder = 0

2112 ÷ 32 

Quotient = 66, Remainder = 0

2112 ÷ 48 

Quotient = 44, Remainder = 0

So, the answer is correct.