Question

Find the shortest length of a pipe that can be measured exactly with 4m, 6m and 9m long measuring tapes respectively.​

Answer 1

$\Large{\underbrace{\underline{\sf{Understanding\; the\; Question}}}}$

Here in this question, concept of LCM is used. We are given 3 pipes of length 4m, 6m and 9m. We have to find the shortest length of pipe that will be measured by each of these pipes. We can find the required length of pipe by finding LCM of these 3 pipes.

So let's start!!

Let's make the given length of pipe in the form of exponents.

• 4m=2²

• 6m=2×3

• 9m=3²

Since 2²×3²=36 is the highest factor of these numbers, it is the LCM.

So the required length of pipe is 36m.

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Verification:

Let's check if 36 is multiple of given numbers.

• For 4m

36m÷4m=9

Since 4m Divide 36m completely, it is a multiple.

• For 6m

36m÷6m=6

Since 6m divide 36m completely, it is a multiple.

• For 9m

36m÷9m=4

9m also divides 36m, so it is also a multiple.