Since, multiples of 2 as well as of 5 = LCM of (2, 5) = 10

Multiples of 2 as well as of 5 from 1 and 500 is 10, 20, 30, …., 500.

Clearly this is an AP with common difference, d = 10

And first term, a = 10

Let the no if terms in this AP are n

Then,

a_n = a + (n - 1)d

500 = 10 + (n - 1)10

490 = (n - 1)10

n - 1 = 49

n = 50

now, Sum of this AP

[ as last term is given]

= 25[ 10 + 500]

= 25(510)

= 12750