Each of the series S1 = 2 + 4 + 6 + ......... and S2 = 3 + 6 + 9 + ......... is continued
to 100 terms. Find how many terms are identical.

The identical terms will be of the form k*LCM(d1,d2) +smallest common number .

Where d1 , d2 are common differences in two series and smallest common term in two series = 6

So N= k*LCM ( 2,3) + 6

N= 6k+6   (where k is a whole number)

Since the last number in 1st series is 200 and last number in 2nd series is 300, it is sufficient to check multiples of till 200

Therefore total number of multiples of 6 below 200 = 33