Problem:

When john sorts his collection of computer card games into groups of 3, 4, 5 or 8, there is always one card left. what is the smallest number of cards John can have?

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- Sep 7th 2012, 06:15 AMrcsPROBABILITY on number of cards.
Problem:

When john sorts his collection of computer card games into groups of 3, 4, 5 or 8, there is always one card left. what is the smallest number of cards John can have? - Sep 7th 2012, 06:42 AMHallsofIvyRe: PROBABILITY on number of cards.
If we let N be the number of cards we are looking for then n= 3i+ 1, n= 4j+ 1, n= 5k+ 1, n= 8l+ 1. (This is equivalent to saying that N is "equal to 1 modulo 3, 4, 5, 8".)

We can, for example, set n= 3i+ 1= 4j+ 1= 5k+ 1= 8l+ 1 so that 3i= 4j= 5k= 8l. From "4j= 8l", we must have = 2l so we can reduce that to 3i= 5k= 8l. Now, what are the smallest possible values of i, k, and l so that those are true? That is, what is the smallest number that k is a multiple of 3, 5, and 8? - Sep 7th 2012, 06:57 AMrcsRe: PROBABILITY on number of cards.
Im just so confused, according to the book from i got this problem is 121, i dont know how the author obtained it

- Sep 7th 2012, 07:10 AMHallsofIvyRe: PROBABILITY on number of cards.
You have posted a large number of widely varying problems without showing any attempt of your own on any of them. As far as this problem is concerned, if you cannot find "the smallest number that k is a multiple of 3, 5, and 8", you should not even be attempting these problems.

Do you see that 3, 5, and 8 have no divisors in common? So knowing**that**what is the smallest number that has is a multiple of 3, 5, and 8. - Sep 7th 2012, 08:42 AMSorobanRe: PROBABILITY on number of cards.
Hello, rcs!

Quote:

When John sorts his collection of computer card games into groups of 3, 4, 5 or 8,

there is always one card left. .What is the smallest number of cards John can have?

The least common multiple (LCM) of {3, 4, 5, 8} is 120.

The number of computer card games is: .$\displaystyle 120 + 1 \:=\:121.$

Do you see why?

- Sep 8th 2012, 05:11 AMrcsRe: PROBABILITY on number of cards.
thanks a lot Prof. Soroban. You are a big Help :)

- Sep 8th 2012, 05:48 AMHallsofIvyRe: PROBABILITY on number of cards.