What is the smallest number that is divisible by all integers from 1 to 10?

2520 (number) is:

1-The smallest number divisible by all integers from 1 to 10, i.e. it is their least common multiple.

2-The product of five consecutive numbers, namely 3×4×5×6×7.

3-The last highly composite number which is half of the next highly composite number (5040).The highly composite number is any positive integer which has at least as many divisors as any smaller positive integer.

4-The last highly composite number that is a divisor of all following highly composite numbers.

5-It is multiplied by the numbers:7×30×12, which represents the number of days of the week, the number of days of the month (as-suming that the month is usually 30 days), and the months of the year.

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12 Comments

Nickey Welsh

Ray Anderson, Yes that's how I did it. add the integers up came to 9 , 9 is divisible by 3 so the complete number is.

dejayel

Ray Anderson, That's how I got it right too.

Ray Anderson

2520 is the only one divisible by 3

Fred Zeb Fudpucker

"Figure out the prime factors of each of the numbers 1-10. 1 = 1*1. 2 = 2*1. 3 = 3*1. 4=2*2. 5 = 5*1. 6 = 2*3. 7= 7*1. 8 = 2*2*2. 9 = 3*3. 10 = 2*5. The smallest number that is divisible by all of these has to contain all of these factors. So 2^3 * 3^2 * 5 * 7, or 2520. (I confess that it surprises me that it's that high. But that's what the math shows.)"---Edward Sherry