What is the smallest integer that is divisible by the first 10 positive integers?

The smallest integer that is divisible by the first 10 positive integers (1 through 10) is known as the least common multiple (LCM) of those numbers. The LCM of 1 through 10 is 2520. This is found by taking the highest powers of all prime factors present in the factorizations of these integers. Thus, 2520 is the smallest integer divisible by all of them.