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Q: In how many ways can 75 be express as the sum of at least two positie integers all of which are consecutive?

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The least of the three integers is 26.

25, 26 and 27.

-4, -2, 0, and 2 are the four consecutive even integers. When you add them up they equal -4.

17 , 19 , 21 and 23 are the odd integers whose sum is 80 and the least integer is 17

You need 5.

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The LCM of consecutive integers is their product. Consecutive integers will not both be multiples of seven.

-13, -15 and -17

63

3 and 5.

There are no three odd consecutive integers because consecutive integers all have 1 between them, meaning at least one of them will be an even integer. ------------------- Let x, x+2, and x+4 be the three consecutive odd integers. We want x+(x+2)+(x+4) to equal 531. x+(x+2)+(x+4) = 531 3x+6=531 3x=531-6=525 x=525/3=175 Therefore, the three consecutive odd integers are 175, 177, and 179. A quick check shows that those three integers add up to 531.

The LCM of 20 and 21 is 420. The LCM of any pair of consecutive integers is their product.

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