Both the sequences are in arithmetic progression. The common difference (d1) for the first sequence =4 The common difference (d2) for the first sequence =5 The first term common is 19. The common terms will also be in arithmetic progression with common difference LCM(d1,d2)=LCM(4,5)=20 Let there be 'n' terms in this sequence, then the last term would be ≤415 i.e. a+(n−1)d≤415 ⇒19+(n−1)×20≤415 ⇒(n−1)×20≤415−19 ⇒(n−1)×20≤396 ⇒(n−1)=[‌
396
20
] where [ n] is the greatest integer ⇒(n−1)=19 ⇒n=20