Answer:
The statement "There is an integer that is divisible by 6 and is also divisible by 8, but is not divisible by 48." is true.
Step-by-step explanation:
Consider the provided information.
We need to prove that there exist an integer that is divisible by 6 and is also divisible by 8, but is not divisible by 48 with the help of an example.
The prime factors of the number 6 is:
6 = 2 × 3
The prime factors of the number 8 is:
8 = 2 × 2 × 2
Now the Least Common Multiple of the number 6 and 8 is:
2 × 2 × 2 × 3 = 24
Since, it is clear that the number 24 is divisible by 6 and 8 but the number is not divisible by 48.
There exist infinite numbers which can be divisible by 6 and 8 but not divisible by 48.
All the odd multiples of 24 are divisible by 6 and 8 but all the odd multiples of 24 are not divisible by 48.
For example:
24 × 3 = 72 (The number is divisible by 6 and 8 but not divisible by 48.)
24 × 5 = 120 (The number is divisible by 6 and 8 but not divisible by 48.)
Hence, the statement "There is an integer that is divisible by 6 and is also divisible by 8, but is not divisible by 48." is true.
