Math, asked by jyotiiii2021, 1 month ago

The 5 digit greatest number, which is divisible by 12, 18 and 24, is:
(a)99996
(b)99972
(c)99936
(d)99960​

Answers

Answered by pulakmath007
6

SOLUTION

TO CHOOSE THE CORRECT OPTION

The 5 digit greatest number, which is divisible by 12, 18 and 24, is

(a)99996

(b)99972

(c)99936

(d)99960

EVALUATION

Here the given numbers are 12 , 18 , 24

Now

12 = 2 × 2 × 3

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

So LCM

= 2 × 2 × 2 × 3 × 3

= 72

Now the greatest 5 digit number = 99999

If we divide 99999 by 72 we get 1388 as Quotient and 63 as Remainder

Hence the required 5 digit greatest number, which is divisible by 12, 18 and 24

= 99999 - 63

= 99936

FINAL ANSWER

Hence the correct option is (c) 99936

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Answered by PADMINI
6

Given:

The 5 digit greatest number, which is divisible by 12, 18 and 24, is:

Solution:

LCM of 12, 18, and 24:

\begin{array}{r | l} 2 & 12, 18, 24 \\  \cline{2-2} 2 & 6, 9, 12 \\ \cline{2-2} 2 & 3, 9, 6 \\ \cline{2-2} 3 &3, 9, 3 \\ \cline{2-2} 3 & 1, 3, 1 \\ \cline{2-2}  & 1, 1, 1 \end{array}

LCM = 2 x 2 x 2 x 3 x 3 = 72

The Greatest 5-digit number is 99999

when we divide the greatest 5-digit number 99,999 by 72 we get 63 as Remainder.

Subtract the remainder 63 from the greatest 5-digit number.

=> 99999 - 63

=> 99936

So, The 5 digit greatest number, which is divisible by 12, 18 and 24, is 99936

Hence, The required answer is 99936

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