LCM of two or more numbers is divisible by their HCF.
Idea: Write the numbers using their HCF, then look at the LCM.
Let the two numbers be \(a\) and \(b\). Let their HCF be \(H\) and their LCM be \(L\).
We can write:
\( a = H \cdot a_1 \)
\( b = H \cdot b_1 \)
Here, \(a_1\) and \(b_1\) have no common factor (they are co-prime).
Then the LCM is:
\( L = H \cdot a_1 \cdot b_1 \)
Now divide \(L\) by \(H\):
\( \dfrac{L}{H} = a_1 \cdot b_1 \)
The right side is a whole number. So, \(L\) is divisible by \(H\).
Quick example: Take 12 and 18.
HCF \(= 6\), LCM \(= 36\).
\( 36 \div 6 = 6 \) (a whole number)
Therefore, the statement is true.