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 Find the smallest positive multiple of 21 that has no digit smaller than 5.

 Jul 3, 2021
 #1
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according to this website, https://www.mathwarehouse.com/answered-questions/multiples/what-are-the-multiples-of-21-solved.php all the multiples of 21 are:

 

$ 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029 $

 

we can right away cancel all the ones which are $< \: 500$ right?

 

its just easy from here -- looking from the left to the right we have to find which number has no figures $< \: 500$ :

 

$  \color{black}{504, 525, 546,} \color{royalblue}{567}   \color{black}{,588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029   } $

 

so your answer is $\boxed{\color{royalblue}{567}}$

 Jul 3, 2021

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