Help me solve this question please
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Help me solve this question please
x divided by 2 leaves a remainder of 1.
x divided by 3 leaves a remainder of 2.
x divided by 4 leaves a remainder of 3.
x divided by 5 leaves a remainder of 4.
x divided by 6 leaves a remainder of 5.
Find the smallest value of x.
Is there a method to solve such problems or just trial and error, using (LCM -1) ?
x divided by 3 leaves a remainder of 2.
x divided by 4 leaves a remainder of 3.
x divided by 5 leaves a remainder of 4.
x divided by 6 leaves a remainder of 5.
Find the smallest value of x.
Is there a method to solve such problems or just trial and error, using (LCM -1) ?
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Re: Help me solve this question please
Yup, LCM of 2, 3, 4, 5 and 6, take away 1. Hopefully not too much trial and error involved there? 2 and 3 go into 6, so they're covered. LCM of 4 and 6 is 12. LCM of 12 and 5 is 60.
Re: Help me solve this question please
Writing out the values for 6 doesn't take long.
11, 17, 23, 29, 35, 41, 47, 53, 59
Divide by 5 and look at remainders.
R1, r2, r3, r4, r0, repeat
Divide by 4
R3, r1,r3, r1
Solution found very quickly
11, 17, 23, 29, 35, 41, 47, 53, 59
Divide by 5 and look at remainders.
R1, r2, r3, r4, r0, repeat
Divide by 4
R3, r1,r3, r1
Solution found very quickly
Re: Help me solve this question please
Thanks 'Aliportico' and 'moved'.
I was wondering if there is a generic formula, (LCM-n) where n is the remainder or some relation between divisor and remainder.
I was wondering if there is a generic formula, (LCM-n) where n is the remainder or some relation between divisor and remainder.
Re: Help me solve this question please
Developing systematic methods and reasoning in maths is essential. Solving problems such as this require a logical approach and no more really. If we teach a bunch of formulae then we are just giving children more and more to remember. Maths is fundamentally an approach to problem solving.
Re: Help me solve this question please
Agreed, that is what/how maths should be. However, in a time constrained exam where passing the exam is the only goal, temptation to find a short cut/ formula takes over the fundamentals.