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!

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- Jun 5th 2007, 10:14 AM #1

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- Jun 5th 2007, 10:19 AM #2

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- Jun 5th 2007, 11:07 AM #3

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Originally Posted by**Neils Henrik Abel**

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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, 12:13 PM #4

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- Jun 5th 2007, 12:27 PM #5

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

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- Jun 5th 2007, 01:40 PM #7

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- Jun 5th 2007, 01:43 PM #8

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