Identical Terms

Number Theory Level 2

How many terms are identical(same) in two arithmetic progression $2,4,6,8.......$ upto 100 terms and $3,6,9,12.......$ upto 80 terms .

33 50 36 40

1 solution

Kay Xspre
Oct 19, 2015

The series is $2x$ where $1 \leq x \leq 100$ and $3y$ where $1 \leq y \leq 80$ . Finding lowest common denominator of both series will gives $6z$ , when $6z \leq 2\times100 = 200$ . Hence, there will be $\lfloor \frac{200}{6}\rfloor\ = 33$ terms common between the two series

Identical Terms

1 solution

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