SOLUTION: What is the least positive integer that is divisible by all whole numbers 1 to 9?

Question 334676: What is the least positive integer that is divisible by all whole numbers 1 to 9?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If it is divisible by 9, it is also divisible by 3, so include 9 as a factor but exclude 3.

If it is divisible by 8, it is also divisible by 4 and 2, so include 8, but exclude 4 and 2.

You need 7.

If it is divisible by 2 and 3 then it is divisible by 6, so divisibility by 9 and 8 implies divisibility by 6, exclude 6.

You need 5.

Hence, your positive integer must have factors of 9, 8, 7, and 5. You can do the arithmetic.

John

My calculator said it, I believe it, that settles it

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the least positive integer that is
divisible by all whole numbers 1 to 9?
-----
Find the least common multiple:
1 = 1
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2*3
7 = 7
8 = 2^3
9 = 3^2
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Select each prime factor present in its highest factor:
2^3 ; 3^2, 5, 7,
---
Form the product: 8*9*5*7 = 2520
====================================
Cheers,
Stan H.

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