Name: Questions based on LCM and HCF
Uploaded: 2019-07-19
Duration: 27 min 33 s
Description: Watch this session to learn the approach to solve some very interesting questions based on HCF and LCM...

Question

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.

Accepted Answer

Given that, $2$ is divisible by both $3 .$ and $3 .$ It is also divisible by $2 \times 3 = 6 .$

We know that if a number is divisible by two co-prime numbers then it is divisible by their product also.

Since $2$ and $3$ are co-primes, so, the number which is divisible by both $2$ and $3$ , is also divisible by $2 \times 3 = 6 .$

But, $4$ and $6$ are not co-primes, because $4$ and $6$ has $2$ as common factor.

For example, $12$ is divisible by both $4$ and $6$ .

But $12$ is not divisible by $4 \times 6 = 24$ .

Similarly, $36$ is divisible by both $6$ and $4$ .

But $36$ is not divisible by $4 \times 6 = 24$

Therefore, the given statement is incorrect.

Note: take your own examples according to given conditions and justify the answer.

$18$ 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.

Important Questions on Playing with Numbers

Learn and Prepare for any exam you want !

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.

Important Questions on Playing with Numbers

Learn and Prepare for any exam you want !

$18$ 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.