Math Is Fun Forum

balasvce

Member

Registered: 2006-12-20

Posts: 37

solve & explain

all positive integers 1 to 600 divisible by 4,5 and 14 respectively

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: solve & explain

This is quite easy...

The 5 and the 14 make things quite simple.

70, 140, 210, 280, 350, 420, 490 and 560 are all multiples of both 14 and 5 at the same time. Now the only easy bit is to get rid of all the ones which aren't divisible by 4:

140, 280, 420, 560.

Notice the patterns?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: solve & explain

Devanté's got it. For this kind of question, you need to find the lowest common multiple of all of the numbers you're given. If you then need to find all of the multiples up to a certain point, then you just list all the multiples of the lowest common multiple until you get high enough.

4, 5, and 14 only have one common factor: the 4 and 14 share a factor of 2.
Therefore, the lowest common multiple of these is 4*5*14/2 = 140.
The multiples up to 600 are therefore 140, 2*140, 3*140, 4*140. And this matches Devanté's list.

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Why did the vector cross the road?
It wanted to be normal.