10 people make a new years resolution to swim, the first person will swim every day, the 2nd every 2nd day, the 3rd every 3rd day what will be the next day that all 10 swim together? How do we work this out?
2006-10-04 09:02:29 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The answer is the least common multiple (LCM) of 1,2,3,4,5,6,7,8,9 and 10.
To compute the LCM of two numbers a and b, you can use the formula LCM(a,b)=a*b/GCD(a,b), where GCD is the greatest common divisor.
Proceed like this:
LCM(1,2)=2.
LCM(2,3)=6.
LCM(6,4)=12.
LCM(12,5)=60.
and so on. You'll find that this will have to be a multi-year resolution, because they won't all swim together for more than 365 days.
2006-10-04 09:09:12 · answer #1 · answered by James L 5 · 0⤊ 1⤋
we have to find the least common multiple of numbers from 1 to 10 :)
Common myltiple of these numbers is for sure :
10!=1x2x3x4x5x6x7x8x9x10= 3628800
to make it least common multiple in a easy way, because it is not very big number in this case, we can reduce some numbers, which happen again:
because 1x2x3x4x5x6x7x8x9x10= 1x2x3x2x2x5x2x3x7x2x2x2x3x3x2x5
so
1x2x2x2x3x3x5x7 = 2520 will still be divisible be all the numbers from 1 to 10.
This means that the first day,when all 10 people will swim together will be in 2520 days :)
2006-10-05 19:01:44 · answer #2 · answered by Alicja K 1 · 0⤊ 0⤋
I couldn't tell you the answer myself because i don't have time to work it out but you need to write down the multiples of each number and the day they swim together will be when all the numbers can go into that day number. The number which all these are factors for in other words.
2006-10-04 16:18:53 · answer #3 · answered by Mash 2 · 0⤊ 1⤋
What we need to do is find a number x such that
x = 1x = 2a = 3b = 4c = 5d = 6e = 7f = 8g = 9h =10i.
Now wat we do is elimanate the common factors. leavein us with
x = 5 x 7 x 8 x 9 = 2520
So the first time they will all swim together is 2520 days after new years day, which works out to be between the 20th and 24th nov (6 years later) depending onhow the leap years come.
2006-10-04 16:59:52 · answer #4 · answered by hackmaster_sk 3 · 0⤊ 1⤋
No Factors
2...............2
3...............3
4...............2 x 2
5................5
6................2 x 3
7................7
8................2 x 2 x 2
9................3 x 3
10...............2 x 5
cancel out = 2 x 3 x 2 x 5 x 7 x 2 x 3 = 2520 days
so every 2520 days they would swim together or once in just over seven years only.
2006-10-04 21:57:19 · answer #5 · answered by Tropic-of-Cancer 5 · 1⤊ 0⤋
Thursday
Only kidding, go with James L he has given the correct way of working it out.
2006-10-04 16:08:44 · answer #6 · answered by dobbie 2 · 0⤊ 1⤋
get the other two to start swimming everyday
2006-10-04 16:05:15 · answer #7 · answered by Anonymous · 0⤊ 1⤋
1st of January
2006-10-05 03:47:32 · answer #8 · answered by spongebbob79 2 · 0⤊ 1⤋
you find a number that they all go into.
2006-10-04 16:05:11 · answer #9 · answered by ToniLianne 4 · 0⤊ 1⤋
the first day...
2006-10-04 16:04:18 · answer #10 · answered by danielencarla 2 · 0⤊ 1⤋