A number is divisible by 4 and 12. Is it necessary that it will be divisible by 48? Give another example in support of you answer. [3 MARKS]

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Solution

Concept: 2 Marks
Example: 1 Mark

$48 = 4 \times 12$

4 and 12 are not co-prime

Therefore, it is not necessary that the number will be divisible by 48.

Let us consider the number 72 for an example

$72 \div 4 = 18$ , so 72 is divisible by 4.

$72 \div 12 = 6$ , so 72 is divisible by 12.

But 72 is not divisible by 48.

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Q. A number is divisible by 4 and 12. Is it necessary that it will be divisible by 48? Give another example in support of you answer. [3 MARKS]

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

A number is divisible by 4 and 12. Then, it should definitely be divisible by 48.

Q. If a number is divisible by 3 and 4, then it is also divisible by 12.

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A number is divisible by 4 and 12. Is it necessary that it will be divisible by 48? Give another example in support of you answer. [3 MARKS]

Concept: 2 Marks Example: 1 Mark 48=4×12 4 and 12 are not co-prime Therefore, it is not necessary that the number will be divisible by 48. Let us consider the number 72 for an example 72÷4=18, so 72 is divisible by 4. 72÷12=6, so 72 is divisible by 12. But 72 is not divisible by 48.