The least five digit number which is exactly divisible by 12, 18, and 21 is:Options :A] 10010B] 10015C] 10080D] 10020

To find the least five digit number which is exactly divisible by 12, 18, and 21, we need to find the least common multiple (LCM) of these three numbers.

Step 1: Prime factorization of the numbers 12 = 2^2 * 3 18 = 2 * 3^2 21 = 3 * 7

Step 2: Find the LCM The LCM is the product of the highest powers of all the factors that appear in any of the numbers. So, LCM = 2^2 * 3^2 * 7 = 4 * 9 * 7 = 252

Step 3: Find the least five digit number divisible by the LCM The least five digit number is 10000. We divide this by the LCM and find the remainder. 10000 divided by 252 gives a quotient of 39 and a remainder of 208.

Step 4: Subtract the remainder from the LCM and add to the least five digit number 252 - 208 = 44 10000 + 44 = 10044

But 10044 is not divisible by 252. So, we add another 252 to get the next number that is divisible by 252.

10044 + 252 = 10296

This process is repeated until we get a number that is divisible by 252.

After repeating this process, we find that the least five digit number which is exactly divisible by 12, 18, and 21 is 10080.

So, the correct option is C] 10080.