question_answer 1)

18 is divisible by both 2 and 3. It is also divisible by \[2\times 3=6.\] Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by \[4\times 6=24?\] If not, give an example to justify your answer.                

Answer:

                We know that, if a number is divisible by two co-prime numbers, then it is divisible by their product also. Here, 2 and 3 are co-prime numbers. So, 18 is divisible by their product i.e. 6 but 4 and 6 are not co-prime numbers, so the number divisible by 4 and 6 will not be divisible by  \[4\times 6=24.\] e.g. Take the number 60. It is divisible by both 4 and 6, but it is not divisible by its product. i.e.\[~6\times 4=24\]