The lest number
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Rezaul Haque
- Posts:1
- Joined:Sat Jan 01, 2011 3:45 pm
Well my problem is pretty much simple! But the problem is that I can't deduce the logical steps required. So please help. Now let's return to the problem: What is the least number which when divided by 18, 24, & 36 yield remainders of 12,18, & 30 respectively!!!
Re: The lest number
The solution is .
At first you need to find $lcm(18,24,36)$
then try all $36p+30$ for $p=1,2,3,....$ in $lcm(18,24,36)$ range for a possible solution.
It's my method. other people may have better solutions!
At first you need to find $lcm(18,24,36)$
then try all $36p+30$ for $p=1,2,3,....$ in $lcm(18,24,36)$ range for a possible solution.
It's my method. other people may have better solutions!
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Re: The lest number
There certainly is a better way. Observe that the desired remainders are just $6$ less than the divisors.
$12 = 18 - 6$
$18 = 24- 6$
$30 = 36 -6$
The desired number is just $-6 modulo 18, 24, 36$. This means this numbers can be represented in the form $18a - 6$ or, $24b - 6$ or, $36c -30$, where $a,b,c$ are positive integers.
Such a number is $LCM(18,24,36) - 6 = 66$
$12 = 18 - 6$
$18 = 24- 6$
$30 = 36 -6$
The desired number is just $-6 modulo 18, 24, 36$. This means this numbers can be represented in the form $18a - 6$ or, $24b - 6$ or, $36c -30$, where $a,b,c$ are positive integers.
Such a number is $LCM(18,24,36) - 6 = 66$
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor
Re: The lest number
I was wondering why the moderators did not move this post to correct forum...Anyway, Rezaul: please post your problems in correct forum. (Read the forum guide for more info).
Welcome, anyway.
Welcome, anyway.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.