Expert: Chanda Walker - 2/4/2009

Question
what is the four consecutive multiples of 15 whose sum is three time the lcm of 10 and 22? I thought it was three

Answer
lcm do you mean lowest common multiple?

consective multiples of 15 are:

15, 30, 45, 60 . . ..

so we can write that algebraically like this:

15*(x)
15*(x+1)
15*(x+2)
15*(x+3)

And we want to sum that so . . .

15*(x+x+1+x+2+x+3)

15*(4x + 6)

That is 3 times the lcm of 10 and 22.

The lcm of 10 and 22 is 110.

FINALLY our equation to solve is:

15*(4x + 6) = 3* 110

60 x + 90 = 330
60x = 240
x = 4

So the multiples are:

60, 75, 90, 105

Let's check that.

The sum of those are 330.

So yep that is the answer.