What is the largest 5-digit number divisible by 16, 24, and 36?

a)
99952

b)
99920

c)
99984

d)
99936

Correct answer is option 'D'. Can you explain this answer?

Question

What is the largest 5-digit number divisible by 16, 24, and 36?a)99952b)99920c)99984d)99936Correct answer is option 'D'. Can you explain this answer?

Answer

The largest 5-digit number=99999
LCM of 16 ,24 and 36=144
The largest 5-digit digit number that divisible by 16, 24 and 36=99999÷144×144
= 694 x 144
= 99936
So, Option D is correct answer.

Answer

LCM of 16, 24, and 36 is 144. Largest 5-digit number is 99952.

Answer

To find the largest 5-digit number divisible by 16, 24, and 36, we need to find the least common multiple (LCM) of these numbers first.First, let's find the LCM of 16, 24, and 36:Prime factorization:( 16 = 2^4 )( 24 = 2^3 	imes 3 )( 36 = 2^2 	imes 3^2 )To find LCM:Take the highest powers of all prime factors:Highest power of 2: ( 2^4 )Highest power of 3: ( 3^2 )Therefore, [ 	ext{LCM}(16, 24, 36) = 2^4 	imes 3^2 = 16 	imes 9 = 144 ]Now, we find the largest 5-digit number divisible by 144. This involves finding the largest integer ( n ) such that ( n ) is divisible by 144 and ( n ) is a 5-digit number.Largest 5-digit number is 99999.Find the largest ( n ) divisible by 144 less than or equal to 99999: [ n = \left\lfloor \frac{99999}{144} ightfloor 	imes 144 ]Calculate: [ \left\lfloor \frac{99999}{144} ightfloor = 694 ] [ n = 694 	imes 144 ] [ n = 99936 ]Thus, the largest 5-digit number divisible by 16, 24, and 36 is ( \boxed{99936} ).

Answer

Approach:
To find the largest 5-digit number divisible by 16, 24, and 36, we need to find the least common multiple (LCM) of these numbers and then find the largest 5-digit number that is divisible by this LCM.

Calculating LCM:
- LCM of 16 and 24 is 48 (16 x 3 = 48, 24 x 2 = 48).
- LCM of 48 and 36 is 144 (48 x 3 = 144, 36 x 4 = 144).
Therefore, the LCM of 16, 24, and 36 is 144.

Finding the largest 5-digit number:
The largest 5-digit number is 99999. To find the largest 5-digit number divisible by 144, we need to find the largest multiple of 144 that is less than 99999.
Dividing 99999 by 144 gives us 694 with a remainder.
Therefore, the largest 5-digit number divisible by 144 is: 144 x 694 = 99936.

Conclusion:
The largest 5-digit number that is divisible by 16, 24, and 36 is 99936 (option D).

Answer

Th largest five digit number is 99999 LCM of 16,36 and 24- 144 the largest 5 digit number that is divisible by 16,24 and 36=99999÷144×144 =694×144. =99936.

the option number d is correct

Answer

THE LCM 16, 24 ABD 36 IS 99936.
SO THE CORRECT ANSWER IS OPTIONS D

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