Question

Find the greatest number of 4 digits which is exactly divisible by 2, 3,
8 and 10.​

Answer 1

Step-by-step explanation:

To find a number exactly divisible by 2,3,8 & 10 . We have to

1) take LCM of the given number i.e.

L.C.M of 2,3,8,10 is 120

2) check the 10's multiple of 120 in such a way that

(a) for finding greater the 10's multiple would be 1 times more i.e. if finding greatest number of 4 digit go for fifth and later subtract the required multiple of 120 from the answer to get the highest 4th digit number.

(b)for finding lowest check if the LCM has first digit greater than 5 .. if yes go with 5 multiples else 10 multiples.

Now we have to find the 4th greatest number

so , LCM of 2,3,8,10 is 120

(a) 120 × 100 = 12000 (which is of 5 digits)

we need just a number divisible by 120 just greater than 2000 so,

120 × 17 = 2040

Thus ,

We can say (12000-2040) is also a multiple of 120 i.e. 9960 is the greatest number of 4 digits divisible by 2,3,8,10