What is the 5 digit smallest number?

Complete step-by-step answer:
The Largest 5-digit number is 99,999 and the Smallest 5-digit number is 10,000
When we subtract the Largest 5-digit number with the Smallest 5-digit number then
$99,999 - 10,000 = 89,999$
The difference between the Largest 5-digit number with the Smallest 5-digit number is 89,999
Here option B is the correct answer.

Note: - For solving such types of problems we must read the question nicely. Many times, it is said that the number must be unique. Then in this case the largest and the smallest digit number changes. But in this there was nothing mentioned like that.

Complete step-by-step answer:
Given numbers are 72 and 108.
We have to find out the L.C.M of these numbers.
L.C.M is called the least common multiple.
The least common multiple (LCM) of any two numbers or more than two numbers is calculated as first list all the prime factors of each number, then multiply each factor the greatest number of times it occurs in the numbers. If the same factor occurs more than once in the given numbers then we have to multiply the factor the greatest number of times it occurs.
Therefore, first calculate the factors of the first number i.e. 72. So, the factors of 72 are,
$72 = 1 \times 2 \times 2 \times 2 \times 3 \times 3$
Now calculate the factors of the second number i.e. 108. So, the factors of 108 are
$108 = 1 \times 2 \times 2 \times 3 \times 3 \times 3$
The L.C.M of the given numbers according to above definition is calculated as
L.C.M = $1 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$ = 216
So the L.C.M of 72 and 108 is $= 216$
Now we have to find the smallest 5 digit number that is divisible by that is exactly divisible by 72 and 108.
So the smallest 5 digit number should be the multiple of LCM of $72$ and $108$ (i.e. 216).
Now as we know that the smallest five digit number is $10000$.
Now divide this number by $216$ we have,
$ \Rightarrow \dfrac{{10000}}{{216}} = 46\dfrac{{64}}{{216}}$
So as we see that the quotient is $46$ and remainder is $64$.
So the number which is exactly divisible by $216$ is $(10000 – 64) = 9936$.
Now in this number add $216$, which is the required smallest $5$ digit number which is exactly divisible by $72$ and $108$.
So the smallest $5$ digit number is $= 9936 + 216 = 10152$.
Therefore, the smallest 5 digit number that is exactly divisible by $72$ and $108$ is $10152$.

Note: Whenever we face such types of questions first find out the LCM of the numbers then write the smallest 5 digit number (i.e. 10000) then divide this number by 216 and note down the remainder, then subtract this remainder from the smallest 5 digit number then add the LCM value in the resultant number of the given numbers and simplify which is the required answer.

In this problem, we need to make a five-digit number. And the first thing we can say about it is that all of its digits need to be different. Because we’re trying to make the smallest five-digit number, this means then that we need to use the smallest five digits. So that’s zero, one, two, three, and four. If we replace any of these five digits with any of the other digits, then our number isn’t going to be the smallest possible number anymore. To make the smallest possible number, we have to use these five digits.

A five-digit number means there are five different places where we could put our digits. From left to right, these have the value of 10 thousands. This is the place with the greatest possible value, thousands, hundreds, tens, and ones. This is the place with the lowest possible value. If we look at the way we’ve written our digits to start with, we can see these are in order, from smallest to largest. So surely, if we’d like to make the smallest five-digit number, we should write our digits in the same order from smallest to largest in our place value grid. This way, we put the lowest possible value in our 10 thousands column, the next lowest value in our thousands column, and so on.

Now, this isn’t the right answer. But it’s almost correct. If we try to read this number, it’s not actually a five-digit number. The zero in the 10 thousands column doesn’t stand for anything. So our number is actually 1234. It’s a four-digit number. For our number to be a true five-digit number, we need to put a digit that stands for something other than zero in our 10 thousands place. But remember, we do want it to be as small as possible. What if we swap around the zero and the one. We now have one lot of 10 thousand and zero thousands. And importantly, we now have a five-digit number. Our digits are in order from left to right from smallest to largest, with one exception. We’ve swapped the zero and the one around so that we actually make a five-digit number.

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