Math Is Fun Forum

Cammun

Guest

Euler Student Problems. Least Common Multiples?

Hi,

I have found some working for a question I am working on. I have written the question and the working below. Can someone please explain it to me?

QUESTION:

The parliament of the land Achronia consists of two houses. The parliament was elected in 1995 for a period of four years beginning on Monday, January 1st, 1996, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every 10 days for the duration of the term, and the meetings of the second house must occur every twelve days. For example the second meetings of the first and the second houses were held on the 11th and 13th of January respectively. A new law can be passes only when both houses meet on a Monday. How many opportunities will the parliament members have to pass new laws during this four year term?

WORKING:

opportunities
= [(4*365 + 1) / (7*LCM of 10 and 12)]
= [1461 / (7*60)]
= [1461 / 420]
= 3

answer = 4, if we include the first session on Monday, January 1st, 1996.

Please Help!:dunno

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Euler Student Problems. Least Common Multiples?

So there is an opportunity for a new law to be passed every 420 days.

There are 1461 days in the four-year term.

∴ the answer is 4 (including Monday 1 January 1996).

Last edited by JaneFairfax (2008-09-25 02:19:09)