# Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.

Correct result:

R =  946

#### Solution:

$A=135 \ \\ B=315 \ \\ \ \\ 135=3^3 \cdot 5 \ \\ 315=3^2 \cdot 5 \cdot 7 \ \\ LCM(135, 315)=3^3 \cdot 5 \cdot 7=945 \ \\ \ \\ x=LCM(A,B)=LCM(135,315)=945 \ \\ \ \\ R=x+1=945+1=946$

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Math student
Calculatin is all wrong.
Smallest number after 1 is 2 .
And 2 also give me the remainder 1.
135/2 and 315/2 calculate yourself.

Dr Math

2:135 is 0 and reminder 2 !!!

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