ST wrote:what is the least positive integer that is divisible by each of the integers 1 thorough 7, inclusive?
a. 420
b. 840
c. 1260
d. 2520
e. 5040
Could someone please explain this? I am having hard time understanding OG's explanation? Thanks
ST
We're asked to find the lowest common multiple ("LCM") of the integers 1 through 7.
We know that 7! = 5040 will be a multiple of all 7, but that doesn't mean it's the lowest common multiple. The only time that the LCM and the multiple of a set of numbers is the same is when those numbers have no common prime factors.
There are many approaches we could take to find the LCM; as usual, some basic math and common sense/logic provides an efficient approach.
Let's take a quick peek at the set:
{1, 2, 3, 4, 5, 6, 7}
All of our primes must be included... so we're going to need a 2, 3, 5 and 7 among our factors.
1 is just 1 - we can ignore it.
4 = 2*2. We have one 2 already, so we need a second 2 to ensure that 4 is a factor of our number.
6 = 2*3. Since we already have a 2 and a 3, we can ignore 6.
Therefore, the LCM is 2*3*5*7*2 = 420.
