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The smallest number that is exactly divisible by every number from 1 to 10 is:
A1260
B5040
C3600
D2520
Answer & Solution
Correct answer: D. 2520
1. The smallest such number is the LCM of 1 through 10.
2. Take the highest power of each prime up to 10: 2^3 from 8, 3^2 from 9, then 5 and 7.
3. So the LCM = 8 x 9 x 5 x 7.
4. That is 72 x 35 = 2520.
5. 1260 fails on 8, and 5040 and 3600 are larger than needed, so only 2520 is the smallest.
_Source: NCERT Class 10 Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_
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