Question

Find the least length of a rope which can be cut into several pieces of length 18 metres, 24 metres and 12 meters length.​

Answer 1

Answer:

$\huge {\boxed {\green {Answer:}}}$

We need to find the least length of a rope which can be cut into several pieces of length 18 metres, 24 metres and 12 meters length.

For these types of questions, we need to understand the nature of the question. In the, question they ask for such a length of rope which will be the shortest length for any rope to be divided into several pieces of length 18 metres, 24 metres and 12 meters length.

So, in this case, if we find out the LCM of 18, 24 and 12, will get our answer.

So, LCM of 18, 24 and 12

$\huge {\underline {2 | 18, 24, 12}}$

$\huge {\underline {3 | 09, 12, 06}}$

$\huge {\underline {2 | 03, 04, 02}}$

$\huge {\underline {\:\:\:03, 02, 01}}$

LCM = 72

Thus required answer = 72 metres

If it would have been written '...maximum length of rope which can be used to measure several...' instead of '...least length of a rope which can be cut into several...' in the question, then we would have to find out the HCF instead of LCM.

Hope you liked my answer, thanks for posting :)