Free Printable WorksheetMathGrade 5Math Curriculum5.24

5.24 Identify Multiples and Common Multiples Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 5 Math worksheet provides structured practice on 5.24 Identify Multiples and Common Multiples. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Skill description: Select the correct answer when generating and identifying multiples of a whole number and recognize common multiples of two numbers in context. Choose the statement that best justifies the answer using place-value language and an estimation check. Corresponding standards: Not listed in source.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 5

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 5.24 Identify Multiples and Common Multiples skill assessments:

Problem 1Difficulty: Mastery

Ivy wrote a puzzle number: 1□28. The completed number is a common multiple of 16 and 36. Which statement best justifies the digit that goes in the box so the number becomes 1728?

AThe digit is 3, making 1328. Place value: 1328 has 1 thousands, 3 hundreds, 2 tens, and 8 ones. Estimation check: 1300 is close, so it should divide by 16 and 36.

BThe digit is 6, making 1628. Place value: 1628 has 1 thousands, 6 hundreds, 2 tens, and 8 ones. Estimation check: 1600 is close, so it should divide by 16 and 36.

CThe digit is 8, making 1828. Place value: 1828 has 1 thousands, 8 hundreds, 2 tens, and 8 ones. Estimation check: 1800 is close, so it should divide by 16 and 36.

DThe digit is 7, making the number 1728. 1728 ÷ 16 = 108 and 1728 ÷ 36 = 48, so it is a common multiple. Place value: 1728 has 1 thousands, 7 hundreds, 2 tens, and 8 ones. Estimation check: 20×100 is close to 1728.

Solution & Explanation:Fill the box to match 1728. Then verify: 1728 is divisible by both 16 and 36. Place value: 1728 has 1 thousands, 7 hundreds, 2 tens, and 8 ones. Estimation check: rounding the factors still gives a product close to 1728.

Problem 2Difficulty: Mastery

In the art room, Ivy designs a repeating display: one cycle every 35 steps and another every 42 steps. Which statement best justifies a common step number between 2395 and 2645 where BOTH cycles start together?

A2555 is common because it is close to a multiple of each number. 2555 has 2 thousands, 5 hundreds, 5 tens, and 5 ones. Estimation check: close is good enough.

B2562 works for both since 2562 ÷ 35 = 72 and 2562 ÷ 42 = 62. 2562 has 2 thousands, 5 hundreds, 6 tens, and 2 ones. Estimation check: the quotients look close.

CCommon step numbers are multiples of the LCM of 35 and 42. The LCM is 210. 2520 is 210 × 12 and it is in the interval. Place value: 2520 has 2 thousands, 5 hundreds, 2 tens, and 0 ones. Estimation check: 200×12 is close to 2520.

D2519 works because it is close to 2520. Place value: 2519 has 2 thousands, 5 hundreds, 1 tens, and 9 ones. Estimation check: close numbers have close results.

Solution & Explanation:Find the LCM of 35 and 42: 210. Then check multiples of 210 until one is in the interval; 2520 works. Place value: 2520 has 2 thousands, 5 hundreds, 2 tens, and 0 ones. Estimation check: 200×12≈2520.

Problem 3Difficulty: Mastery

In a community garden, Fatima designs a repeating display: one cycle every 22 steps and another every 32 steps. Which statement best justifies a common step number between 3078 and 3293 where BOTH cycles start together?

A3167 works because it is close to 3168. Place value: 3167 has 3 thousands, 1 hundreds, 6 tens, and 7 ones. Estimation check: close numbers have close results.

BCommon step numbers are multiples of the LCM of 22 and 32. The LCM is 352. 3168 is 352 × 9 and it is in the interval. Place value: 3168 has 3 thousands, 1 hundreds, 6 tens, and 8 ones. Estimation check: 400×9 is close to 3168.

C3190 works for both since 3190 ÷ 22 = 144 and 3190 ÷ 32 = 100. 3190 has 3 thousands, 1 hundreds, 9 tens, and 0 ones. Estimation check: the quotients look close.

D3200 is a common multiple because 22 × 146 = 3200 and 32 × 99 = 3200. 3200 has 3 thousands, 2 hundreds, 0 tens, and 0 ones. Estimation check: 22×146≈3212.

Solution & Explanation:Find the LCM of 22 and 32: 352. Then check multiples of 352 until one is in the interval; 3168 works. Place value: 3168 has 3 thousands, 1 hundreds, 6 tens, and 8 ones. Estimation check: 400×9≈3168.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 5 Math students. It aligns with educational standard 5.24 (Identify Multiples and Common Multiples).