Problem 36E

Let m and n be positive integers and let k be the least common multiple of m and n. Show that mZ ∩ nZ = kZ.

36. Let m and n be positive integers and let k be the least common multiple of m and n. Show that .

Step By Step Solution

Step 1 of 2

Given k is the least common multiple of m and n.

Also we know any set of the form is ideal, so and are ideals.

( the set of integers. If is any integer, we write for the set .)