{Next week|On Saturday}, `person(1)` is having a party, and `he(1)` plans to serve hot dogs in buns. {`He(1)` is also planning to play `his(1)` `randRange(2,30)` favorite songs. |}`He(1)` does not want to have any food left over.

Hot dogs come in packages of `A`, and buns come in packages of `B`.

**What is the minimum amount of hot dogs and buns person(1) can buy?**

`LCM`

To find the minimum amount of hot dogs and buns `person(1)` can buy, we need to find the least common multiple of the number of hot dogs per package (`A`) and the number of buns per package (`B`).

The least common multiple is the smallest number that is a multiple of `A` and `B`.

We know that `A` x `B` (or `PRODUCT`) is a common multiple, but is it the least common multiple?

Write out the multiples of `BIGGER` until we find a number divisible by `SMALLER`.

`\text{``M`}

`\text{``M`}

,
So, `LCM` is the least common multiple of `A` and `B`.

**The smallest amount of food person(1) can buy is LCM hot dogs and buns**, or

`person(1)` is organizing a {baseball|softball} league, and `he(1)` needs to purchase jerseys and visors for the players. Jerseys come in sets of `A`, and visors come in sets of `B`.

`person(1)` does not want to have any jerseys or visors left over.

**What is the minimum number of jerseys and visors person(1) can purchase?**

`LCM`

To find the minimum number of jerseys and visors `person(1)` can purchase, we need to find the least common multiple of the number of jerseys per set (`A`) and visors per set (`B`).

The least common multiple is the smallest number that is a multiple of `A` and `B`.

We know that `A` x `B` (or `PRODUCT`) is a common multiple, but is it the least common multiple?

Write out the multiples of `BIGGER` until we find a number divisible by `SMALLER`.

`\text{``M`}

`\text{``M`}

,
So, `LCM` is the least common multiple of `A` and `B`.

**At a minimum, person(1) needs to purchase LCM jerseys and visors**, or

`person(1)` and `person(2)` both teach `course(1)` at `school(1)`. They give their students the same number of total `exam(1)` questions each year.

Each `exam(1)` `person(1)` gives contains `A` questions, and each `exam(1)` `person(2)` gives has `B` questions on it. {`person(1)` has `randRange(15,40)` students in `his(1)` class.|`person(2)` also assigns `randRange(3,10)` projects per year.}

**What is the minimum number of total exam(1) questions person(1) and person(2) each give their students in a year?**

`LCM`

To find the minimum number of questions `person(1)` and `person(2)` give, we need to find the least common multiple of the number of questions on `person(1)`'s tests (`A`) and `person(2)`'s tests (`B`).

The least common multiple is the smallest number that is a multiple of `A` and `B`.

We know that `A` x `B` (or `PRODUCT`) is a common multiple, but is it the least common multiple?

Write out the multiples of `BIGGER` until we find a number divisible by `SMALLER`.

`\text{``M`}

`\text{``M`}

,
So, `LCM` is the least common multiple of `A` and `B`.

**The least number of questions person(1) and person(2) each give is LCM**, or

At a track and field competition, there are `A` sprinters and `B` long-distance runners{ and `randRange(5,100)` fans|}. All teams need to have the same number of sprinters and the same number of long-distance runners.

**What is the greatest number of teams that can be formed?**

`GCD`

To find the greatest number of teams that can be formed, we need to find the greatest common divisor of the number of sprinters (`A`) and long-distance runners (`B`).

The greatest common divisor is the largest number that is a factor (or divisor) of both `A` and `B`.

The only factor (divisor) of 1 is 1.

The factors (divisors) of `A` are `A_FACTORS`.

The only factor (divisor) of 1 is 1.

The factors (divisors) of `B` are `B_FACTORS`.

So, the greatest common divisor of `A` and `B` is `GCD`.

`\gcd(`

`A`, `B`) = `GCD`

**The greatest number of teams that can be formed is plural(GCD,"team")**, with

People who eat at `person(1)`'s famous dessert restaurant expect consistency, so `person(1)` must ensure that every plate of cookies is {exactly the same|identical}.

`person(1)` bakes one batch of `A` chocolate-chip cookies and one batch of `B` oatmeal cookies each day; since `person(1)` bakes cookies fresh daily, `he(1)` does not want any cookies left over at the end of the night.

**What is the greatest number of plates of cookies person(1) can serve on one night?**

`GCD`

To find the greatest number of cookie plates that can be served, we need to find the greatest common divisor of the number of chocolate-chip cookies per batch (`A`) and oatmeal cookies per batch (`B`).

The greatest common divisor is the largest number that is a factor (or divisor) of both `A` and `B`.

The only factor (divisor) of 1 is 1.

The factors (divisors) of `A` are `A_FACTORS`.

The only factor (divisor) of 1 is 1.

The factors (divisors) of `B` are `B_FACTORS`.

So, the greatest common divisor of `A` and `B` is `GCD`.

`\gcd(`

`A`, `B`) = `GCD`

**The greatest number of cookie plates that can be served is plural(GCD, "plate")**, with

`person(1)` wants to create identical sets of office supplies for all of `his(1)` coworkers, with at least 1 `deskItem(1)` and `deskItem(2)` in each. Each `deskItem(1)` comes in a package of `A`, and each `deskItem(2)` comes in a package of `B`.

`person(1)` wants to use one entire package of each item.

**What is the greatest number of sets of office supplies person(1) can make?**

`GCD`

To find the greatest number of sets of office supplies that `person(1)` can make, we need to find the greatest common divisor of `A` (since each `deskItem(1)` comes in a package of `A`) and `B` (since each `deskItem(2)` comes in a package of `B`).

The greatest common divisor is the largest number that is a factor (or divisor) of both `A` and `B`.

The only factor (divisor) of 1 is 1.

The factors (divisors) of `A` are `A_FACTORS`.

The only factor (divisor) of 1 is 1.

The factors (divisors) of `B` are `B_FACTORS`.

So, the greatest common divisor of `A` and `B` is `GCD`.

`\gcd(`

`A`, `B`) = `GCD`

**The greatest number of office supply sets that can be created is plural(GCD,"set")**, with