Tip #11 to Get a Top ACT Math Score

Almost every ACT has a "multiples" question. We know the recipe for the ACT, one multiples question, one average question, etc. These 50 Skills review exactly what you need. Multiples are great to review; you knew this inside-out back in 5th grade. Mrs. Shortino taught it, you did the 7 minutes of homework, and then went straight to the kickball field. Now, you haven't thought about multiples for 6 years. So, here's a quick review, and guess what, now that you're older, anything that seemed hard in 5th grade will be easy!

Multiples—All the numbers that are divisible by a certain number. Example: The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, etc.

Least common multiple—The lowest number that is a multiple of several numbers. Example: What is the least common multiple of 10, 15, and 20 ?

The trick to finding the least common multiple is to list the multiples of the largest given number and then choose the lowest one that is also a multiple of the other given numbers. This is a great trick; we start with the biggest number because it has fewest multiples to consider and will save time and energy.

So to find the least common multiple of 10, 15, and 20, list the multiples of 20: 20, 40, 60, 80, 100. And choose the first one that is also a multiple for both 10 and 15. The number 60 works because it is the lowest number on the list that is a multiple of 10, 15, and 20.

Of course, for most questions, you'll also just be able to "Use the Answers," which will probably be even faster. Note: You can use this same strategy when an ACT question asks for the lowest common denominator; it's basically the same thing.

Let's look at this question:

Solution: This question could be difficult, but "Use the Answers" makes it easy! Just test each answer choice by dividing it by 30, 40, and 50. The number 600 is the lowest number on the list that is divisible by 30, 40, and 50. Notice that 1200 works also, but 600 is the lowest. Make sure to try all choices.

Correct answer: C

Example Problems

Easy

What is the lowest number that is a multiple of 10, 12, and 15 ?
1. 1800
2. 900
3. 120
4. 60
5. 30

Medium

126 is the least common multiple for which pair of numbers?
1. 2 and 62
2. 9 and 14
3. 6 and 22
1. 3 and 42
2. 5 and 25
What is the least common multiple of 60, 50, and 80 ?
1. 60
2. 120
3. 1002
4. 1200
5. 12000
If m and p are positive integers, what is the least common multiple of 4, 3m, 5p, and 6mp ?
1. 30mp
2. 60mp
3. 60mp²
1. 120mp
2. 120m²p

Hard

A bag of peanuts could be divided among 8 children, 9 children, or 10 children with each getting the same number, and with 2 peanuts left over in each case. What is the smallest number of peanuts that could be in the bag?
1. 722
2. 362
3. 182
4. 56
5. 29

Answers

Answer to Brian's Math Magic Trick #1—Multiples: You said carrot. How did I guess your vegetable? Check out my website for answers: www.BrianLeaf.com/carrot

D This question could be difficult, but "Use the Answers" makes it easy! Just test each answer choice by dividing it by 10, 12, and 15. The lowest choice that is divisible by 10, 12, and 15 is 60. Notice that several other answers work also, but 60 is the lowest. Make sure to try all choices.
G "Use the Answers."
1. 2 and 62—1cm = 62
2. 9 and 14—1cm = 126
3. 6 and 22—1cm = 66
1. 3 and 42—1cm = 42
2. 5 and 25—1cm = 25
D "Use the Answers" and it's easy! Just try each answer choice by dividing it by 60, 50, and 80. Choices A, B, and C don't even divide evenly by the three numbers—they are not multiples for all three. Choice D works, all three numbers divide evenly (without a decimal or fraction) into 1200. Choice E works also, but D is the lowest answer.
G "Use the Answers" and it's easy! Just try each answer choice by dividing it by 3, 4, 5, and 6, and then make sure there's an m and a p in there. Choice F doesn't divide evenly by 4. And choices H and K have more m's or p's than we need—we only need one of each. Choice J works, but G is the lowest answer. If that seems confusing, you can also "Make It Real" (Skill 18). Just choose easy numbers for m and p, such as 2 and 3, and then test the answers to find the least common multiple. Nice!
B This "superhard" question is easy for us. The hardest part for most kids is knowing what to do to solve it, i.e. recognizing it as a least common multiple question. But we know that every ACT has one, and we are watching for it, so we identify it and know what to do. Then just "Use the Answers," although you have to take the two peanuts off before you test each choice to see if it is the least common multiple. Choice B is correct since 362 – 2 = 360 which is the least common multiple of 8, 9, and 10.

Go to: Tip #12

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