# Computing greatest common divisor and least common multiple

1. Each row in the following table contains values for the integers a and b. In this table, the value of r is the remainder (from the Division Algorithm) when a is divided by b. Complete each row in this table by determining gcd(a, b), r, and gcd(b, r).

a b gcd(a, b) Remainder r gcd(b, r)

44 12

75 21

50 33

2. Formulate a conjecture based on the results of the table in Part (1).

3. Find two rational numbers with denominators 9 and 15, respectively, whose sum is equal to 10/225 or explain why it is not possible to do so.

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#### Solution Preview

1. Each row in the following table contains values for the integers a and b. In this table, the value of r is the remainder (from the Division Algorithm) when a is divided by b. Complete each row in this table by determining gcd(a, b), r, and gcd(b, r).

a b gcd(a, b) Remainder r gcd(b, r)

44 12 4 8 ...

#### Solution Summary

The solution gives detailed steps on computing a greatest common divisor and a least common multiple. This solution is 218 words and includes calculations.