The least number that is divisible by all the numbers from $1$ to $10$ (both inclusive) is:
(a) $10$
(b) $100$
(c) $504$
(d) $2520$
Step-by-Step Solution
Key Concept: The required number is $\text{LCM}(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)$.
Prime factorisation of numbers 1 to 10: $1=1, 2=2, 3=3, 4=2^2, 5=5, 6=2\times3, 7=7, 8=2^3, 9=3^2, 10=2\times5$. [0.5 Mark]
$\text{LCM} = 2^3 \times 3^2 \times 5 \times 7 = 8 \times 9 \times 5 \times 7 = 2520$. [0.5 Mark]
---
🎯 Official CBSE Marking Scheme:
Correct prime factorisation setup: 0.5 Mark
Correct LCM calculation: 0.5 Mark
Correct Answer: $2520$