Every 3rd locker was jammed
every 8th locker was not painted on the inside
every 10th locker had a loose screw
a: what is the condition of locker 12.
b: what is the first locker to have two problems.
c: what is the first locker to have all three problems.
d: how many lockers did the custodians have to fix in a

A) Locker 12 is jammed because every third locker is jammed. So you just lit out the multiples of 3 which are: {3, 6, 9, 12, ...}.

This locker was painted inside because 12 is not a multiple of 8 and does not have a loose screw because 12 is not a multiple of 10.

There is only one problem with locker number 12.

B) The first locker to have two problems would be the 24th locker. Those two problems being that it's jammed and isn't painted inside.

Note how 24 is the LCM of 3 and 8, but 24 is not a multiple of 10 so it doesnt have a loose screw.

LCM = lowest common multiple.

C) The first locker to have all three problems would be the 120th locker.

The number 120 is the LCM of the set {3,8,10}. This is equivalent to finding the LCM of the set {24,10}. To find the LCM between 24 and 10, list out all the multiples of each til you see that 120 is the lowest shared common multiple between the two lists. Or you can multiply out 24 and 10 to get 24*10 = 240, then divide by the GCF 2 to get 240/2 = 120.

D) It does not say how many lockers there are in total, so this question cannot be answered. More information is needed. It seems like part D has been cut off based on what you wrote.

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step-by-step explanation: