The sum of the common terms of the following three arithmetic progressions.
 3, 7, 11, 15, ………., 399; 
2, 5, 8, 11, ………., 359 and 
2, 7, 12, 17, ………, 197 is equal to ______

Let 3 A.P’s are 
S₁ : 3, 7, 11, 15, ……, 399 with common difference 4 = d₁ 
S₂ : 2, 5, 8, 11, ……, 359 with common difference 3 = d₂ 
S₃ : 2, 7, 12, 17, ……,197 with common difference 5 = d₃ 
Common difference of A.P. formed by common terms of ${\mathrm{S}}_1, {\mathrm{S}}_2, \mathrm{and} {\mathrm{S}}_3$ is D 
= L.C.M. of (d₁, d₂, d₃) = 60 
So series S₄ : 47, 107, 167
$\therefore$Sum of common terms of S₄ is $\frac{3}{2}(47+107+167)=321$