What is the least number that is exactly divisible by all the numbers from 1 to 10?

Step 1 (LCM Concept): The least positive integer divisible by all numbers from 1 to 10 is the Least Common Multiple (LCM) of the set $\{1,2,3,4,5,6,7,8,9,10\}$.

Step 2 (Prime Factorization of each number):

• $1=1$

• $2=2^1$

• $3=3^1$

• $4=2^2$

• $5=5^1$

• $6=2\times 3$

• $7=7^1$

• $8=2^3$

• $9=3^2$

• $10=2\times 5$

Step 3 (Form the LCM): Take the highest power of each prime appearing in these factorizations:

• For 2: $2^3=8$

• For 3: $3^2=9$

• For 5: $5^1=5$

• For 7: $7^1=7$

Thus, the least positive integer is $2520$.