NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False Questions

Question 97

Step 1: Understand LCM

LCM means Least Common Multiple. It is the smallest number that both numbers divide exactly.

We write it as \(\text{LCM}\).

Step 2: Compare LCM with the larger number

The LCM is at least the larger number.

So, LCM is either:

• equal to the larger number, or
• greater than the larger number.

Step 3: When is LCM equal to the larger number?

If one number divides the other, then:

\( \text{LCM} = \text{larger number} \).

Example: \(4\) and \(8\)

Since \(8\) is a multiple of \(4\),

\( \text{LCM}(4,8) = 8 \) (equal to the larger number).

Step 4: When is LCM greater than the larger number?

If neither number divides the other, then:

\( \text{LCM} > \text{larger number} \).

Example: \(4\) and \(6\)

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

Conclusion

The statement says: “LCM is greater than the larger number.”

This is false because sometimes the LCM is equal to the larger number (when one divides the other or when the numbers are equal).