Question

find the greatest 4 digit number which exactly divides 8 12 20​

Answer 1

Step-by-step explanation:

Firstly we will find out the LCM of 8, 12 & 20 

8= 2×2×2

12= 2×2×3

20=2×2×5

Lcm= 2××2×2×3×5= 120

Greatest 4 digit number is 9999

Then divide this number by LCM of 8, 12 & 20 9999/120 will get remainder 39

now subtract 39 from the 4 digit number

9999 – 39 = 9960

9960 is the greatest number 4-digit number divisible by 8, 12 ,&20

Answer 2

First, we need to find the LCM of 8, 12 and 20.

$\begin{array}{r | l} 2 & 8,12,20 \\ \cline{2-2} 2 & 4,6,10 \\ \cline{2-2} & 2,3,5 \\ \end{array}$

LCM of 8, 12 and 30 is ⇒ $\sf \bf 2\times 2 \times 2 \times 3\times 5 = 120$

We know that the greatest 4 digit number is 9999.

So now we need to find the remainder when we divide 9999 and 120.

We get the remainder as 39.

Now we have to subtract 39 from 9999.

We get ⇒ $\sf 9999-39 =9960$

∴We can say that 9960 is the greatest 4 digit number which is divisible by 8, 12 and 20.