Question

find the greatest 4 digit number which is exactly divisible by 20 , 24 , and 120 ( answer - 9960 ) explain it​

Answer 1

Answer:

ANSWER

L.C.M of 8, 12, 15, 20 = 120 Greatest number of 4-digits = 9999

∴ Greatest number of 4-digits exactly divisible by 120 = 9999 - 39 = 9960

Answer 2

Concept

Mathematicians use a set of precise rules called the "divisibility rules" to determine whether a given integer is divisible by a certain number or not. A divisibility rule is a type of shortcut that enables us to determine, without actually completing the division operation, whether a given integer is divisible by a certain number by looking at its digits.

GIven

numbers = 20,24 and 120

Find

the largest four-digit integer that can be divided into the aforementioned numbers exactly.

Solution

To solve this, we'll apply the LCM principle.

We must find the LCM of the given integers in order to get the largest four-digit number that is exactly divisible by 20, 24, and 120.

we get the LCM of the numbers as = 2×2×5×6 = 120

Since we already know that 9999 is the largest four-digit number, we will divide 9999 by the derived LCM, which is 120.

since the remainder is not 0, hence we subtract 39 from 9999.

9999 ₋ 39 = 9960, which is the multiple of 120 and is exactly divisible.

Now, 120×83 = 9960

we see that the greatest 4 digit number is 9960 , which is exactly divisible by the given numbers.

hence the greatest number is 9960.

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