The HCF of two or more numbers is greater than their LCM.
Step 1: Recall meanings
\(\text{HCF}\) means the greatest number that divides all the given numbers.
\(\text{LCM}\) means the smallest number that is a common multiple of all the given numbers.
Step 2: General idea
For any natural numbers \(a\) and \(b\):
\(\text{HCF}(a,b) \le a\) and \(\text{HCF}(a,b) \le b\).
Also, \(a \le \text{LCM}(a,b)\) and \(b \le \text{LCM}(a,b)\).
So overall, \(\text{HCF}(a,b) \le \text{LCM}(a,b)\).
Step 3: Example to see it
Take \(4\) and \(6\).
\(\text{HCF}(4,6) = 2\).
\(\text{LCM}(4,6) = 12\).
Here, \(2 \le 12\), not greater.
Step 4: When can they be equal?
If the numbers are the same, say \(n\) and \(n\), then
\(\text{HCF}(n,n) = n\) and \(\text{LCM}(n,n) = n\).
They are equal, but still not “HCF greater than LCM”.
Conclusion
The statement is false because in general \(\text{HCF} \le \text{LCM}\) (equality only when the numbers are equal).