Q: Prove if a|k, b|k, then lcm(a,b)|k.

(Hint: LCM of non-zero intergers a and b is the smallest postive integer m such that a|m, b|m)

Please help!

Results 1 to 8 of 8

- Jun 5th 2007, 09:14 AM #1

- Joined
- Mar 2006
- Posts
- 705
- Thanks
- 2

- Jun 5th 2007, 09:19 AM #2

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Jun 5th 2007, 10:07 AM #3

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

Originally Posted by**Neils Henrik Abel**

---

Let then that means:

Now, by the above statements,

**Definition:**Let . For we define so that .

**Theorem:**Let and . Then .

**Proof:**Again, just follow the definitions.

Substitute second equation into first,

Since we have,

- Jun 5th 2007, 11:13 AM #4

- Joined
- Mar 2006
- Posts
- 705
- Thanks
- 2

- Jun 5th 2007, 11:27 AM #5

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Jun 5th 2007, 12:01 PM #6

- Joined
- Mar 2006
- Posts
- 705
- Thanks
- 2

- Jun 5th 2007, 12:40 PM #7

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Jun 5th 2007, 12:43 PM #8

- Joined
- Mar 2006
- Posts
- 705
- Thanks
- 2