The sum of the common terms of the following three arithmetic...

We have,

${S}_{1}: 2, 5, 8, 11, . . . , 359$

Common difference is ${d}_{1} = 3$

${S}_{2}: 3, 7, 11, 15 . . . , 399$

Common difference is ${d}_{2} = 4$

${S}_{3}: 2, 7, 12, 17 . . . , 197$

Common difference is ${d}_{3} = 5$

Now taking $LCM$ of common difference we get,

$LCM\left({d}_{1}, {d}_{2}, {d}_{3}\right) = 60$

So, common terms are $47, 107, 167$,

Hence, the sum will be $47 + 107 + 167 = 321$.