Explanation:

- Two numbers differ by 20. Let's call them $x$ and $y$ such that $x-y=20$.

- The Least Common Multiple (LCM) is 240. This is the smallest number divisible by both.

- The Highest Common Factor (HCF) is 20. This is the largest number that divides both.

- The relationship between the LCM and HCF of two numbers is given by $LCM\times HCF=x\times y$.

- Substituting the given values: $240\times 20=x\times y$.

- From this, $x\times y=4800$.

- Solving $x-y=20$ and $x\times y=4800$, the numbers are 40 and 60.

So the greater number is:

Option 4: 60