randRange( 2, 6 ) randRange( 1, 10 ) randRangeExclude( 1, 10, [ START_A ] ) START_A * C START_B * C Math.max( A, B ) Math.min( A, B ) A * B getGCD( A, B ) PRODUCT / GCD getMultiples( BIGGER, LCM )

{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 plural(LCM/A,"package") of hot dogs and plural(LCM/B,"package") of buns.

randRange( 2, 6 ) randRange( 1, 10 ) randRangeExclude( 1, 10, [ START_A ] ) START_A * C START_B * C Math.max( A, B ) Math.min( A, B ) A * B getGCD( A, B ) PRODUCT / GCD getMultiples( BIGGER, LCM )

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 plural(LCM/A,"set") of jerseys and plural(LCM/B,"set") of visors.

randRange( 2, 6 ) randRange( 1, 10 ) randRangeExclude( 1, 10, [ START_A ] ) START_A * C START_B * C Math.max( A, B ) Math.min( A, B ) A * B getGCD( A, B ) PRODUCT / GCD getMultiples( BIGGER, LCM )

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 plural(LCM/A, exam(1)) in person(1)'s class and plural(LCM/B, exam(1)) in person(2)'s class.

randRange( 1, 10 ) randRange( 1, 10 ) randRange( 1, 5 ) A_START * FACTOR B_START * FACTOR getGCD( A, B ) toSentence(getFactors( A )) toSentence(getFactors( B ))

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 plural(A/GCD,"sprinter") and plural(B/GCD,"long-distance runner") each.

randRange( 1, 10 ) randRange( 1, 10 ) randRange( 1, 5 ) A_START * FACTOR B_START * FACTOR getGCD( A, B ) toSentence(getFactors( A )) toSentence(getFactors( B ))

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 plural(A/GCD, "chocolate-chip cookie") and plural(B/GCD,"oatmeal cookie") per plate.

randRange( 1, 10 ) randRange( 1, 10 ) randRange( 1, 5 ) A_START * FACTOR B_START * FACTOR getGCD( A, B ) toSentence(getFactors( A )) toSentence(getFactors( B ))

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 plural(A/GCD,deskItem(1)) and plural(B/GCD, deskItem(2)) per set.