NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks

Question 149

Step-by-step (very simple):

1. Multiple means the result of multiplying a number by 1, 2, 3, …
   Example: for \(4\):
   \(4\times1=4\)
   \(4\times2=8\)
   \(4\times3=12\)
   So, multiples of \(4\) are \(4, 8, 12, 16, \dots\)
2. Common multiples are numbers that appear in the multiples list of all the given numbers.
3. Least means the smallest (the first one you meet when counting up).
4. Therefore, LCM = Least Common Multiple = the smallest number that is a multiple of each given number.

Quick example:

Find LCM of \(4\) and \(6\).

Multiples of \(4\):
\(4,\;8,\;12,\;16,\;20,\;24,\;\dots\)

Multiples of \(6\):
\(6,\;12,\;18,\;24,\;30,\;36,\;\dots\)

Common multiples: \(12,\;24,\;\dots\)

The least (smallest) common multiple is \(12\). So,

\(\text{LCM}(4,6) = 12\)

Key idea: LCM means the lowest of their common multiples.