Math and Arithmetic

# What is the smallest number that can be divisible by all integers?

123 ###### 2010-04-16 12:53:30

There does not exist a number that is divisible by all integers. The opposite is true. The number one can divided into all integers.

🎃
0
🤨
0
😮
0
😂
0

## Related Questions All positive integers are divisible by at least one number. All odd whole numbers are not divisible by 2.The term "whole number" has three distinct definitions, in my experience.- Positive Integers ( 1, 2, 3, ... )- Non-Negative Integers ( 0, 1, 2, 3, ... )- Integers ( ..., -3, -2, -1, 0, 1, 2, 3, ... )The largest whole number that is not divisible by two would be the largest odd number, which is not defined.The smallest Positive Integer which is not divisible by two would be 1.The smallest Non-Negative Integer which is not divisible by two would be 0.The smallest Integer which is not divisible by two would be the most negative odd number, which is not defined.  The smallest number that is divisible by all the numbers 2 through 12 is 27,720. There is no smallest number since if any number is divisible by 8, then 8 less than that number is also divisible by 8 - and that argument continues all the way to minus infinity!The smallest positive number divisible by 8 is 8, itself.  The smallest number which is exactly divisible by all the numbers 1 through 11 is 27,720. The smallest one is 1,008. The largest one is 9,990. In all, there are 500 of them, all of them even numbers divisible by 9. (To find them all, multiply 18 by all integers from 56 to 555.) All integers are divisible. All integers greater than one are divisible by prime numbers. The closest number that I could find is 1080, which is divisible by all numbers except 7. To me, 7 seems to be the hardest of them all to match. With this help, maybe you can figure it out. Jakub Krcma says: Actually, the smallest number divisible by the first ten numbers except 7 is 360 (which is why the circle has 360 degrees). And the smallest number divisible by the first ten numbers except 9 is 840 (a third of 2520, which is the smallest number divisible by the first ten numbers). Pythor says: The smallest natural number divisible by the first ten (10) natural numbers is 2520. All integers are divisible by one. All integers are divisible by 1. All positive integers are divisible by one. A number is divisible by 2 if that number is an even number, which means it ends in 0, 2, 4, 6, or 8. A number is divisible by 3 if the sum of its digits is evenly divisible by 3. All negative integers ending in 5 and 0 are divisible by 5. All integers ending with 5 or 0 are divisible by 5 except 0 on its own Your question doesn't make sense, I'm sorry. Integer means a natural number like 2 or 10 or 1047893671282 or even -1048278163. No number between 20 and 40 is divisible by all 4 numbers. The smallest number divisible by all 4 of those numbers is: 56 The smallest positive number that is divisible by all numbers 1-15 is 360,360. Any multiple of that number (like 720,720 or 1,081,080) will also be divisible by all numbers 1-15. It is the smallest number that is a multiple of all the numbers in the set. Or to put it another way, it is the smallest number divisible by all the numbers in the set. They are a subset of all integers. Each even number is divisible evenly by 2. There are countably infinite such numbers. Only integers (whole numbers) can be primes. A prime is a number that is only divisible by 1 and itself. 43.2 and all other decimal numbers are not divisible by 1.  ###### Math and ArithmeticNumbers School SubjectsAlgebraComputersPrime Numbers Copyright © 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.