**Step 1 — Prime factorise both numbers.**
$$960 = 2^6 \times 3 \times 5 \qquad 240 = 2^4 \times 3 \times 5$$

**Step 2 — LCM = product of the highest power of each prime factor.**
$$\text{LCM} = 2^6 \times 3 \times 5 = 64 \times 15 = 960$$

**Step 3 — Verify (shortcut).**
Since $960 = 240 \times 4$, $240$ is a factor of $960$, so $\text{LCM}(960,240) = 960$.

**Answer : (A) 960**