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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 your answer

Solution:

We will be using the concept of divisibility to solve this.

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

The numbers 2 and 3 are co-prime numbers. Hence, if a number is divisible by 2 and 3, it should also be divisible by their product i.e, 6.

But now, the numbers 4 and 6 are not co-prime numbers as their HCF is not equal to 1. Thus, if a number is divisible by both 4 and 6 it necessarily does not have to be divisible by their product 4 × 6 = 24.

Example: 36 and 48 are divisible by both 4 and 6 but not by 24.

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5 Question 11

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 e×ample to justify your answer

Summary:

18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, if a number is divisible by both 4 and 6, it necessarily does not have to be divisible by their product 4 × 6 = 24 as 4 and 6 are not co-prime numbers.

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