The smallest number that is exactly divisible by every number from 1 to 10 is:

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: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_