Question

(iv) Find the greatest number of 4-digits which is exactly divisible by 40, 48 and 60.
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Answer 1

Answer:

9996

Step-by-step explanation:

The greatest 4-digit number is 9999.  

Let's find the LCM of 40, 48, and 60.

40 = 2 x 2 x 5

48 = 2 x 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

LCM OF 40, 48 & 60 = 2 X 2 = 4

Dividend = Divisor x Quotient + Remainder

Divide 9999 by 4 so that we get the remainder,

9999 = 2499 x 4 + 3

Remainder is 3.  

Now, Subtract the remainder from 9999.

9999 - 3 = 9996

Therefore, The required number is 9996 which is exactly divisible by 40, 48 and 60.

Answer 2

Answer: The required number is 9996 which is exactly divisible by 40, 48 and 60.  The greatest 4-digit number is 9999.  

Now, Find the LCM of 40, 48 and 60.

40 = 2 x 2 x 5

48 = 2 x 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

LCM (40, 48, 60) = 2^2 = 4

Divide 9999 by 4 so that we get the remainder,

9999 = 2499 X 4 + 3

Remainder is 3.

Now, Subtract the remainder from 9999.

9999 - 3 = 9996

Therefore, The required number is 9996 which is exactly divisible by 40, 48 and 60.