Fins the greatest number of 5 digit exactly dividible by 12,15 and 36?

Question

Answer

First we will find the LCM of 12,15 and 36

By prime Factorisation,

12=2*2*3

15=5*3

36=2*2*3*3

Now, LCM= 22*32*5

We will find that the LCM is 180

Now, Largest 5 digit number= 99999

Dividing this number by LCM, we get,

99999/180=555.5

Now we will multiply 180 by 555

We will get 99900

We will check now and observe,

99900/12=8325

99900/15=6660

99900/36=2775

Hence the required 5 digit number is 99900

Answer

Answer

Problem: Find the greatest 5-digit number exactly divisible by 12, 15, and 36.

Solution:
To find the greatest 5-digit number exactly divisible by 12, 15, and 36, we need to find the LCM of 12, 15, and 36.

Finding LCM:
To find the LCM, we prime factorize each number and take the highest power of each prime factor.
- Prime factorization of 12: 2 x 2 x 3
- Prime factorization of 15: 3 x 5
- Prime factorization of 36: 2 x 2 x 3 x 3

Taking the highest power of each prime factor, we get:
- LCM = 2^2 x 3^2 x 5 = 180

Finding the Greatest 5-Digit Number Exactly Divisible by 180:
To find the greatest 5-digit number exactly divisible by 180, we divide 99999 (the largest 5-digit number) by 180 and find the largest quotient that is a whole number.

99999 ÷ 180 = 555.55

The largest whole number quotient is 555.

Therefore, the greatest 5-digit number exactly divisible by 12, 15, and 36 is:

555 x 180 = 99900

Final Answer: The greatest 5-digit number exactly divisible by 12, 15, and 36 is 99900.

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