Always 5 left

Number Theory Level 2

What is the smallest possible positive integer x ( > 5 ) x (> 5) that leaves a remainder of 5 5 upon division by 6 6 , 8 8 , or 33 33 ?

270 272 271 269

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Arron Kau by Arron Kau

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3 solutions

Sunil Pradhan
Oct 5, 2014

When any number divided by various divisors and in each case remainder is same then least number is = LCM of divisors + remainder

LCM of 6, 8, 33 is 264 so required number is 264 + 5 = 269

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Pavita Ardhani
Apr 28, 2014

the least common factors of 6, 8, and 33 is 264 (to find the smallest number). 264+5=269

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S W
Apr 21, 2014

x%6=5 , y%8=5, z%33=5 , hence we need LCM of 6, 8 and 33 that's 264 , hence 264+5 =269

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