Find the smallest number which gives reminder 1, 2 and 3 when divided by 7, 9 and 11?

Find the smallest number which gives reminder 1, 2 and 3 when divided by 7, 9 and 11 respectively? 
Answer: 344

 Let the number be p  
 P/7 = remainder 1  
 P/9 = remainder 2  
 P/11 = remainder 3  
 and  
 2P/7 = remainder 2  
 2P/9 = remainder 4  
 2P/11 = remainder 6  
 Now you can see the pattern   
 Notice that if we add 5 to 2P , these equation will become completely divisible by 7,9 and 11 respectively, i.e. remainder becomes 0.  
 So,  
 2P+5/7 = remainder 0  
 2P+5/9 = remainder 0  
 2P+5/11 = remainder 0  
 this means 2P+5 is divisible by 7,9 & 11. So it will be divisible by 7x9x11=693  
 2P+5 = 693  
 2P = 688  
 P = 344  

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