10 peoplemakenew yrs resolution 1st will swim every day, 2nd swimevery 2nd day& so on.when do all 10swimtog?

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?

Answers:
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.
the first day.
you find a number that they all go into.
get the other two to start swimming everyday
SORRY

NO SPEEK ENGLISH

DO YOU SPEEK SPANISH?
Thursday
Only kidding, go with James L he has given the correct way of working it out.
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.
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.
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.
1st of January
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= 1x2x3x2x2x5x2x3x7x2x2x2x3x3x2x.
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 :)

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