NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Problems and Solutions
Question 197

Question. 197

A van stops every 6th block and a bus every 10th block in a colony of 1 to 100. At which block numbers will both stop?

Answer:

Blocks 30, 60, 90

Detailed Answer with Explanation:

We need blocks where both stop together. That means common multiples of 6 and 10 within 1–100.

  1. Find the LCM of 6 and 10.
    (6 = 2 imes 3)
    (10 = 2 imes 5)
    Take all prime factors once: (2, 3, 5)
    ( ext{LCM} = 2 imes 3 imes 5 = 30)
  2. Common stops are multiples of (30) not more than (100).
    (30 imes 1 = 30)
    (30 imes 2 = 60)
    (30 imes 3 = 90)
    (30 imes 4 = 120) (beyond 100, stop)
  3. So, both stop at blocks (30, 60, 90).
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