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Question

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


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Solution

Step 1: Understanding the property of divisibility.

If a number is divisible by two co-prime numbers, then it is divisible by their product also.

The numbers 2 and 3 are co prime numbers, if 18 is divisible by both 2 and 3, it is also divisible by 2×3=6.

Step 2: Check the divisibility of a number by 4 and 6.

Consider a number 36.

36 is divisible by both 4 and 6, but it is not divisible by their product 4×6=24.

Also, 4 and 6 are not co-prime numbers.

Hence, the answer is justified.


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