2007-10-23 15:06:10 · 5 answers · asked by jjfine96 2 in Science & Mathematics ➔ Mathematics
Um... is 2520 the smallest possibility?
2007-10-23 15:12:55 · update #1
How is 15something---- the smallest if 2520 works as well and is way smaller?
2007-10-23 15:15:51 · update #2
Manuka is right for the reasons stated.
To look at it another way, 2520 does the job. But nothing smaller does the job. Why not? Because anything that does the job has to be divisible by all of:
8
9
5
7
and hence by their product -- which is 2520. And if a number is divisible by 2520 and positive, it's greater than or equal to 2520.
The only really tricky part is, I guess, the "and hence by their product" part. You have to know that if something is divisible by the certain powers of different primes, it's also divisible by the products of those prime powers. Of course, that's the essence of unique factorization.
How big a deal is this? Well, the unique factorizations theorem is called the "Fundamental Theorem of Arithmetic".
2007-10-23 19:59:08 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋
Consider the prime factors. We need 3 factors of 2 because 8 has that many, 2 factors of 3 because 9 has that many, and one factor each of 5 and 7. So the answer is
2^3 . 3^2 . 5 . 7 = 8 . 9 . 5 . 7 = 2520.
2007-10-23 22:14:45 · answer #2 · answered by Scarlet Manuka 7 · 6⤊ 0⤋
1
2007-10-23 22:10:15 · answer #3 · answered by tootoot 3 · 0⤊ 7⤋
2 3 4 5 6 7 8 9 10
smallest number =5*6*7*8*9=15120
2007-10-23 22:13:46 · answer #4 · answered by ptolemy862000 4 · 0⤊ 6⤋
multiply them together and that will give you the least common multiple.
2007-10-23 22:10:24 · answer #5 · answered by a c 7 · 0⤊ 7⤋