Question

Determine the greatest 4-digit number which is exactly divisible by 8,10 and 12.
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Answer 1

Answer:

9960

Step-by-step explanation:

L.C.M of the three numbers is 120

So, to find the greatest 4 digit number divisible by all the three numbers,

Divide 9999(greatest 4-digit number) by the L.C.M (120).

So, we will get a remainder as 39.

Subtract 39 from 9999, we get 9960

Hence, 9960 is the greatest 4-digit number which is exactly divisible by 8,10 and 12.

Hope this is clear.

Answer 2

SOLUTION

TO DETERMINE

The greatest 4-digit number which is exactly divisible by 8 , 10 and 12.

EVALUATION

Here the given numbers are 8 , 10 and 12

We prime factorise the given numbers

8 = 2 × 2 × 2

10 = 2 × 5

12 = 2 × 2 × 3

LCM = 2 × 2 × 2 × 3 × 5 = 120

The greatest 4-digit number = 9999

If we divide 9999 by 120 we get 83 as quotient and 39 as the remainder

Hence the required number

= 9999 - 39

= 9960

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