Question

Deepika has more than \[30\] stickers but less than \[40\] stickers. She can pack the stickers into packs of $2,3$ or $4$ without leaving any remainder. How many stickers does she have$?$
$A)36$
$B)37$
$C)33$
$D)39$

Answer 1

Hint: First we have to define what the terms we need to solve the problem are. More than \[30\] and less that \[40\] means she has stickers in-between $31,32,33,34,35,36,37,38,39$ and She can pack the stickers into packs of $2,3$ or $4$ without leaving any remainder, so the greatest common divisor is zero since there is no remainder at the end.

Complete step-by-step solution:
First let us see what is least common multiple, LCM or least common multiple is the simplest method to find out the smallest common multiple between two or more that two numbers. generally, the common multiple is a number which is multiple of two or more than two numbers.
Hence the least common multiple of $2,3$ or $4$(LCM of $2,3,4$) is $12$ (multiple of two times into three times into four)
Thus, now the stickers must be a multiple of $12$ (without leaving any remainder)
As we see the multiple of $12$ is $12,24,36,48,60,....$ (times $1,2,3,4,5,....$)
There are many numbers we can find by multiplying $12$ but the condition is Deepika has more than \[30\] stickers but less than \[40\] stickers. So more than \[30\] and less that \[40\] means she has stickers in-between $31,32,33,34,35,36,37,38,39$
Therefore as we see $36$ is the least common multiple of $12$ ( She can pack the stickers into packs of $2,3$ or $4$ without leaving any remainder) also $36$ is in-between more than \[30\] and less that \[40\].
Hence number of stickers $ = 36$ that means option $A$ is correct
And all other options are wrong because in option
$B)37$ it is not the least common multiple of \[12\]
And in option $C)33$ it is not the LCM of \[12\],
 in option $D)39$ also it is not the LCM of \[12\]
Hence the only correct option is $A)36$.

Note: Greatest common divisor (GCD). If the GCD = 1, the numbers are said to be relatively prime. There also exists a smallest positive integer that is a multiple of each of the numbers, called their least common multiple (LCM).
LCM is used to find out the least common factor or least common multiple of any two or more given integers
More than means $n + 1,n + 2,....$ and less that means $n - 1,n - 2,....$