Question

Two rods of equal length are divided into 250 and 243 equal parts respectively ; if there ends be coincident, find the divisions which are the nearest together.


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Answer 1

Answer:

243rd and 250th division.

Step-by-step explanation:

To answer this question we need to get the least length of the rod.

This requires that we get the LCM of 250 and 243

We get the LCM by prime factorization below :

250 = 2 × 5 × 5 × 5

243 = 3 × 3 × 3 × 3 × 3

The LCM = 3^5 × 5³ × 2 = 60750

For the rod divided into 250 parts each length will be 243 and for the one divided into 243 parts each length will be 250.

When the divisions which are nearest together are the 250th and 243 rd division.