Question

Determine the greatest 3digit number exactly divisible by 8,10 and 12

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The greatest 3digit number exactly divisible by 8,10 and 12

CALCULATION

Here the given three numbers are 8, 10 & 12

Now

$\sf{ 8 = 2 \times 2 \times 2\: }$

$\sf{10 = 2 \times 5 \: }$

$\sf{ 12 = 2 \times 2 \times 3\: }$

$\sf{So \: LCM \: of \: \: 8, 10, 12 \: is }$

$= \sf{ 2 \times 2 \times 2 \times 3 \times 5\: }$

$= \sf{120 \: }$

Now the greatest 3 digit number is 999

If we divide 999 by 120 we get 8 as Quotient and 39 as Remainder

Hence the required greatest 3digit number exactly divisible by 8,10 and 12 is

$= \sf{999 - 39}$

$= \sf{960}$

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LEARN MORE FROM BRAINLY

Out of the following which are proper fractional numbers?

(i)3/2 (ii)2/5 (iii)1/7 (iv)8/3

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Answer 2

Given:

Three numbers are 8, 10 and 12.

To Find:

We need to find out the largest 3-digit number which is exactly divisible by 8, 10 and 12.

Solution:

Firstly we have to calculate the L.C.M. of 8, 10 and 12.

$\[\begin{gathered} 8 = 2 \times 2 \times 2 \hfill \\ 10 = 2 \times 5 \hfill \\ 12 = 2 \times 2 \times 3 \hfill \\ \end{gathered} \]$

L.C.M. of 8,10 and 12 =$\[2 \times 2 \times 2 \times 3 \times 5 = 120\]$

Now we have to find the greatest 3-digit multiple of 120.

Therefore, the number is

$\[\begin{gathered} {\text{12}} \times {\text{8 = 960}} \hfill \\ {\text{12}} \times {\text{10 = 1200}} \hfill \\ {\text{12}} \times {\text{12 = 1440}} \hfill \\ \end{gathered} \]$

 Here, 1200 and 1440 are not 3-digit numbers

Hence, the greatest 3-digit number exactly divisible by 8, 10 and 12 is 960.