Home Link 2 4 Finding Multiples Answers

Home Link 2-4: Finding Multiples — Explained With Answers

Home Link 2-4 in most elementary math programs focuses on finding multiples, and students often get stuck because the idea of a "multiple" feels abstract until it is practiced. This guide breaks the concept into simple steps, shows the methods teachers expect, and walks through the kinds of problems that appear on this assignment with full answers and explanations. Because textbook editions change from year to year, the exact question numbers may differ, but the skills tested are always the same: listing multiples, identifying whether a number is a multiple of another, finding common multiples, and solving simple word problems.

What Is a Multiple?

A multiple is what you get when you multiply a number by a whole number (1, 2, 3, 4, and so on) And that's really what it comes down to..

• Multiples of 5: 5, 10, 15, 20, 25, 30 …
• Multiples of 7: 7, 14, 21, 28, 35, 42 …

Three facts make multiples easy to remember:

1. Every number is a multiple of 1 and of itself.
2. The smallest multiple of a number is the number itself.
3. Multiples never end — you can always multiply by the next counting number.

Three Reliable Ways to Find Multiples

1. Skip Counting

Count by the number. For multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 Worth keeping that in mind. Surprisingly effective..

2. Multiplication Sentences

Write the number times 1, 2, 3, 4…

• 4 × 1 = 4
• 4 × 2 = 8
• 4 × 3 = 12
• 4 × 4 = 16
• 4 × 5 = 20

So the first five multiples of 4 are 4, 8, 12, 16, 20.

3. Division Check (for "Is it a multiple?" questions)

Divide the number in question by the smaller number. If there is no remainder, it is a multiple.

• Is 36 a multiple of 6? 36 ÷ 6 = 6 exactly → Yes
• Is 34 a multiple of 6? 34 ÷ 6 = 5 remainder 4 → No

Common Home Link 2-4 Problem Types, With Answers

Type A: List the first five (or six) multiples

Answer tip: If the directions say "list the first five multiples of 3," do not start with 0 unless your teacher specifically asks for it. Most home links at this level begin with the number itself That's the part that actually makes a difference..

Type B: Circle or list the multiples from a set of numbers

Example: Circle the multiples of 4 in this list: 12, 17, 20, 25, 28, 33, 36, 41, 44.

Answer: 12, 20, 28, 36, 44.

How to check: 4 × 3 = 12, 4 × 5 = 20, 4 × 7 = 28, 4 × 9 = 36, 4 × 11 = 44. The others leave remainders.

Type C: True or false statements

• "24 is a multiple of 6." → True (6 × 4 = 24)
• "30 is a multiple of 9." → False (9 × 3 = 27, 9 × 4 = 36)
• "Every number is a multiple of 1." → True
• "The number 5 is a multiple of 10." →

Type D: Find the next multiple

Example: "What is the next multiple of 7 after 35?"

Answer: 42 Simple as that..

How to think: You know the multiples are 7, 14, 21, 28, 35. The next one is 35 + 7 = 42 Simple, but easy to overlook..

Common Multiples and Least Common Multiple (LCM)

Once you understand multiples, the next step is to find numbers that are multiples of two or more numbers. These are called common multiples But it adds up..

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48…
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54…

Look at the two lists. Day to day, the numbers 12, 24, 36, 48 appear in both lists. These are common multiples of 4 and 6.

The smallest common multiple is called the Least Common Multiple (LCM). For 4 and 6, the LCM is 12 Simple as that..

How to Find the LCM

Method 1: List the Multiples List multiples of each number until you find the first one they share Simple, but easy to overlook. Which is the point..

• Multiples of 3: 3, 6, 9, 12, 15, 18…
• Multiples of 4: 4, 8, 12, 16, 20…
• The first common number is 12, so the LCM of 3 and 4 is 12.

Method 2: Prime Factorization (for larger numbers) Break each number into its prime factors, then multiply the highest power of each prime that appears.

• Find the LCM of 12 and 18.
  • 12 = 2 × 2 × 3
  • 18 = 2 × 3 × 3
  • LCM = 2 × 2 × 3 × 3 = 36

Word Problem Example

Problem: "Sara jumps rope every 4 days. Leo jumps rope every 6 days. If they both jumped today, in how many days will they jump together again?"

Solution: This is an LCM problem. Find the LCM of 4 and 6.

• Multiples of 4: 4, 8, 12, 16, 20…
• Multiples of 6: 6, 12, 18, 24…
• They will jump together again in 12 days.

Putting It All Together

Mastering multiples is more than just memorizing times tables—it’s about building a number sense that helps you see patterns and relationships between numbers. Whether you’re finding common multiples to synchronize events, checking divisibility for a math puzzle, or simply building confidence with arithmetic, these skills form a cornerstone of mathematical fluency. Remember the key steps: skip-count or multiply to list multiples, divide to check for divisibility, and look for shared numbers to find common multiples and the LCM. On the flip side, with practice, these operations become second nature, opening the door to more advanced topics like fractions, ratios, and algebra. The journey from counting by a number to understanding its multiples is a fundamental step in becoming a confident and capable problem-solver.

Try It Yourself

Test your skills with these quick challenges. Answers are below—no peeking until you've tried!

1. List the first five multiples of 9.
2. Is 56 a multiple of 7? How do you know?
3. Find the LCM of 5 and 7.
4. Find the LCM of 8 and 12.
5. Two bells ring at the same time at noon. One rings every 10 minutes, the other every 15 minutes. When will they next ring together?

Answers:

1. 9, 18, 27, 36, 45
2. Yes—56 ÷ 7 = 8 with no remainder, so 56 = 7 × 8.
3. 35 (since 5 and 7 share no common factors, the LCM is simply their product).
4. 24 (multiples of 8: 8, 16, 24…; multiples of 12: 12, 24…)
5. The LCM of 10 and 15 is 30, so the bells ring together again 30 minutes after noon—at 12:30.

Common Mistakes to Avoid

• Confusing LCM with GCF. The LCM is the smallest shared multiple (usually bigger than both numbers); the greatest common factor is the largest shared factor (usually smaller). Read the question carefully.
• Assuming the LCM is always the product. This is only true when the numbers share no common factors. For 4 and 6, the product is 24, but the LCM is just 12.
• Stopping too soon. If you spot a shared number, double-check that no smaller one appears earlier in both lists.
• Forgetting the obvious. Every number is a multiple of itself and of 1, and 0 is technically a multiple of every number—though we usually ignore it when finding the least common multiple.

Where This Leads Next

Multiples and the LCM are not just standalone topics—they reappear constantly. Adding fractions with unlike denominators, for example, depends entirely on this skill: to compute 1/4 + 1/6, you find the LCM of 4 and 6 (which is 12), rewrite the fractions as 3/1

…rewrite the fractions as 3/12 + 2/12 = 5/12. Without the LCM, you'd be stuck adding quarters and sixths as if they were the same size—and they aren't Most people skip this — try not to. That alone is useful..

Beyond fractions, the same idea shows up in surprising places:

• Gears and machinery. If one gear has 8 teeth and another has 12, the same teeth meet again after 24 rotations' worth of turning. Engineers use exactly this reasoning when designing mechanisms.
• Music and rhythm. A pattern repeated every 3 beats layered over one repeated every 4 beats realigns every 12 beats—the LCM again.
• Computer science. Hash tables, scheduling loops, and "every Nth item" logic all lean on divisibility tests and multiples.
• Everyday planning. Buses, class schedules, medication doses, and baking batches all involve events that coincide at LCM intervals.

A few habits that pay off:

• When adding or comparing fractions, don't automatically multiply the denominators. Using the LCM keeps numbers small and saves you simplifying at the end.
• For larger numbers, prime factorization beats long lists. Break each number into primes, then take the highest power of each prime that appears: for 8 (= 2³) and 12 (= 2² × 3), the LCM is 2³ × 3 = 24.
• Check your answer with a quick sanity test: the LCM must be divisible by both original numbers, and it can never be smaller than the larger of the two.

Wrapping Up

Multiples are one of those quiet ideas that seem simple on the surface and turn out to be surprisingly powerful underneath. Consider this: listing multiples trains you to notice structure; divisibility checks teach you to reason about numbers flexibly; and the LCM gives you a tool that works equally well on fractions, calendars, gears, and code. Best of all, the topic rewards exactly the kind of practice that builds lasting fluency—short sessions, lots of small problems, and a habit of asking "does this answer make sense?" before moving on. Master these foundations now, and the next level of math feels less like a wall and more like a doorway It's one of those things that adds up..