If an integer \[k\] is divisible by \[2,5,13\]. What is the next largest number that is divisible by all the \[3\] given numbers?

Hint: Here in this question we know that \[k\] is divisible by\[2,5,13\]and we need to find the largest number that is divisible by all the \[3\]given numbers. As we know that the LCM and multiples of the LCM of the given numbers are divisible by given numbers so we will calculate LCM and multiples of it to get the desired result.

Complete step-by-step answer:
Here the integer \[k\] is divisible by\[2,5,13\]and the next largest number that is divisible by all the \[3\]given numbers has to be found out.
LCM and multiples of the LCM of the given numbers are divisible by given numbers.
Since \[2,5,13\]are co- prime numbers. So we will calculate the LCM of it
\[
   \Rightarrow {\text{LCM of 2,5,13 = 2}} \times {\text{5}} \times {\text{13}} \\
   \Rightarrow {\text{LCM of 2,5,13}} = 130 \\
 \]
It means that some multiples of \[130\] are divisible by the given numbers.
So the required number will be \[k + 130\]and this is the required answer.

Note: Keep in mind that whenever such questions are asked it is usually solved through LCM or HCF. Remember real numbers are those numbers that can be shown on a number line, the integers are types of real numbers and \[k\]is an integer which means it is a real number also. Perform the operations step by step to avoid any calculation mistake