There's Too Many Numbers To List Out!

Number Theory Level 1

3 , 6 , 9 , 12 , 15 , … 5 , 10 , 15 , 20 , 25 , … 7 , 14 , 21 , 28 , 35 , … \begin{aligned} && 3,6,9,12,15,\ldots \\ &&5,10,15,20,25, \ldots \\ &&7,14,21,28,35,\ldots \end{aligned}

The above shows 3 distinct arithmetic progressions . What is the smallest number that appears in all 3 rows?


The answer is 105.

Pi Han Goh by Pi Han Goh , 30, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Ashish Menon
May 23, 2016

The smallest number that appears in all thebthree rows is the lcm of 3, 5 and 7 which is 105 105 . Why? It is because the first progression is the multiples of 3 and the second row is the multiples of 5 and the third row is the multiples of 7. And 105 is the smallest number having all 3,5 and 7 as its factors.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Hana Wehbi
May 22, 2016

L C M ( 3 , 5 , 7 ) = 105 LCM(3,5,7)=105

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...