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LCM Questions and Worksheets by Class and Grade

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LCM questions and worksheets by class and grade, with answers

Six sets of LCM questions with answers, one per class or grade: class 4, 5, 6, 7 and 8, class 10 (India) and grade 6 (US). Every answer is computed, and each set prints as a worksheet with the answers hidden.

Click "answer" to reveal a result. To print a worksheet, use the browser's print command; navigation and answers are removed. The methods behind the questions are on How to find the LCM, and the definition on What is the LCM? Definition, full form, examples.

LCM questions at a glance

SetWhat it covers
Class 4: multiples and first LCMs (numbers 2 to 12)Two numbers, answers by listing multiples.
Class 5: LCM by listing and by division (numbers 4 to 20)Two numbers; the division method may be used.
Class 6: LCM by prime factorisation (numbers 6 to 30)Two numbers; show prime factors (NCERT "Playing with Numbers").
Class 7 and 8: LCM of three numbers (numbers 8 to 60)Up to three numbers; division table with three columns.
Class 10: HCF × LCM problems (numbers 12 to 120)Find the LCM, then check LCM × HCF = product for two numbers.
Grade 6 (US, Common Core 6.NS.B.4): LCM up to 12Two numbers 1 to 12, as in the standard.

Class 4: multiples and first LCMs (numbers 2 to 12)

Two numbers, answers by listing multiples.

  1. Find the LCM of 5, 6.
    answer LCM = 30; HCF = 1; check 30 × 1 = 30
  2. Find the LCM of 4, 11.
    answer LCM = 44; HCF = 1; check 44 × 1 = 44
  3. Find the LCM of 10, 11.
    answer LCM = 110; HCF = 1; check 110 × 1 = 110
  4. Find the LCM of 8, 12.
    answer LCM = 24; HCF = 4; check 24 × 4 = 96
  5. Find the LCM of 8, 9.
    answer LCM = 72; HCF = 1; check 72 × 1 = 72
  6. Find the LCM of 12, 5.
    answer LCM = 60; HCF = 1; check 60 × 1 = 60
  7. Find the LCM of 6, 12.
    answer LCM = 12; HCF = 6; check 12 × 6 = 72
  8. Find the LCM of 5, 3.
    answer LCM = 15; HCF = 1; check 15 × 1 = 15
  9. Find the LCM of 2, 9.
    answer LCM = 18; HCF = 1; check 18 × 1 = 18
  10. Find the LCM of 12, 10.
    answer LCM = 60; HCF = 2; check 60 × 2 = 120

Class 5: LCM by listing and by division (numbers 4 to 20)

Two numbers; the division method may be used.

  1. Find the LCM of 19, 11.
    answer LCM = 209; HCF = 1; check 209 × 1 = 209
  2. Find the LCM of 20, 7.
    answer LCM = 140; HCF = 1; check 140 × 1 = 140
  3. Find the LCM of 6, 10.
    answer LCM = 30; HCF = 2; check 30 × 2 = 60
  4. Find the LCM of 7, 13.
    answer LCM = 91; HCF = 1; check 91 × 1 = 91
  5. Find the LCM of 16, 15.
    answer LCM = 240; HCF = 1; check 240 × 1 = 240
  6. Find the LCM of 18, 4.
    answer LCM = 36; HCF = 2; check 36 × 2 = 72
  7. Find the LCM of 15, 20.
    answer LCM = 60; HCF = 5; check 60 × 5 = 300
  8. Find the LCM of 18, 12.
    answer LCM = 36; HCF = 6; check 36 × 6 = 216
  9. Find the LCM of 19, 15.
    answer LCM = 285; HCF = 1; check 285 × 1 = 285
  10. Find the LCM of 11, 5.
    answer LCM = 55; HCF = 1; check 55 × 1 = 55

Class 6: LCM by prime factorisation (numbers 6 to 30)

Two numbers; show prime factors (NCERT "Playing with Numbers").

  1. Find the LCM of 30, 9.
    answer LCM = 90; HCF = 3; check 90 × 3 = 270
  2. Find the LCM of 21, 29.
    answer LCM = 609; HCF = 1; check 609 × 1 = 609
  3. Find the LCM of 7, 28.
    answer LCM = 28; HCF = 7; check 28 × 7 = 196
  4. Find the LCM of 22, 12.
    answer LCM = 132; HCF = 2; check 132 × 2 = 264
  5. Find the LCM of 18, 17.
    answer LCM = 306; HCF = 1; check 306 × 1 = 306
  6. Find the LCM of 28, 23.
    answer LCM = 644; HCF = 1; check 644 × 1 = 644
  7. Find the LCM of 24, 23.
    answer LCM = 552; HCF = 1; check 552 × 1 = 552
  8. Find the LCM of 13, 7.
    answer LCM = 91; HCF = 1; check 91 × 1 = 91
  9. Find the LCM of 12, 9.
    answer LCM = 36; HCF = 3; check 36 × 3 = 108
  10. Find the LCM of 23, 13.
    answer LCM = 299; HCF = 1; check 299 × 1 = 299

Class 7 and 8: LCM of three numbers (numbers 8 to 60)

Up to three numbers; division table with three columns.

  1. Find the LCM of 12, 50, 49.
    answer LCM = 14,700
  2. Find the LCM of 44, 53.
    answer LCM = 2,332; HCF = 1; check 2,332 × 1 = 2,332
  3. Find the LCM of 29, 38, 13.
    answer LCM = 14,326
  4. Find the LCM of 33, 31, 43.
    answer LCM = 43,989
  5. Find the LCM of 10, 46.
    answer LCM = 230; HCF = 2; check 230 × 2 = 460
  6. Find the LCM of 40, 29, 18.
    answer LCM = 10,440
  7. Find the LCM of 15, 58, 45.
    answer LCM = 2,610
  8. Find the LCM of 27, 35, 55.
    answer LCM = 10,395
  9. Find the LCM of 48, 8, 17.
    answer LCM = 816
  10. Find the LCM of 15, 33, 35.
    answer LCM = 1,155

Class 10: HCF × LCM problems (numbers 12 to 120)

Find the LCM, then check LCM × HCF = product for two numbers.

  1. Find the LCM of 83, 17.
    answer LCM = 1,411; HCF = 1; check 1,411 × 1 = 1,411
  2. Find the LCM of 115, 72, 23.
    answer LCM = 8,280
  3. Find the LCM of 112, 85.
    answer LCM = 9,520; HCF = 1; check 9,520 × 1 = 9,520
  4. Find the LCM of 34, 100.
    answer LCM = 1,700; HCF = 2; check 1,700 × 2 = 3,400
  5. Find the LCM of 41, 68, 110.
    answer LCM = 153,340
  6. Find the LCM of 34, 26, 37.
    answer LCM = 16,354
  7. Find the LCM of 28, 105.
    answer LCM = 420; HCF = 7; check 420 × 7 = 2,940
  8. Find the LCM of 90, 110, 48.
    answer LCM = 7,920
  9. Find the LCM of 102, 47.
    answer LCM = 4,794; HCF = 1; check 4,794 × 1 = 4,794
  10. Find the LCM of 30, 65.
    answer LCM = 390; HCF = 5; check 390 × 5 = 1,950

Grade 6 (US, Common Core 6.NS.B.4): LCM up to 12

Two numbers 1 to 12, as in the standard.

  1. Find the LCM of 5, 10.
    answer LCM = 10; HCF = 5; check 10 × 5 = 50
  2. Find the LCM of 5, 8.
    answer LCM = 40; HCF = 1; check 40 × 1 = 40
  3. Find the LCM of 2, 3.
    answer LCM = 6; HCF = 1; check 6 × 1 = 6
  4. Find the LCM of 9, 2.
    answer LCM = 18; HCF = 1; check 18 × 1 = 18
  5. Find the LCM of 3, 11.
    answer LCM = 33; HCF = 1; check 33 × 1 = 33
  6. Find the LCM of 10, 11.
    answer LCM = 110; HCF = 1; check 110 × 1 = 110
  7. Find the LCM of 3, 5.
    answer LCM = 15; HCF = 1; check 15 × 1 = 15
  8. Find the LCM of 8, 2.
    answer LCM = 8; HCF = 2; check 8 × 2 = 16
  9. Find the LCM of 12, 5.
    answer LCM = 60; HCF = 1; check 60 × 1 = 60
  10. Find the LCM of 10, 3.
    answer LCM = 30; HCF = 1; check 30 × 1 = 30

Worked example for class 10: HCF × LCM

  1. Find the LCM and HCF of 96 and 404. Prime factors: 96 = 2⁵ × 3; 404 = 2² × 101.
  2. HCF = 2² = 4. LCM = 2⁵ × 3 × 101 = 9,696.
  3. Check: 4 × 9,696 = 38,784 = 96 × 404.

LCM questions: how to check an answer

Divide the LCM by each number; every result must be a whole number. Then make sure no smaller number works: if the LCM is even, test half of it against every number. If half fails for any number, the answer is the least common multiple.

HCF and LCM exercises

Mixed questions asking for both are common from class 6 upward. Use the greatest common divisor / GCF / HCF page for the HCF method, and fraction questions on fraction LCM.

Open the LCM Calculator

Frequently asked questions

How do I solve an LCM question in class 5?

List the multiples of each number until one appears in both lists, or use the division method: divide the numbers by primes until every entry is 1 and multiply the divisors. LCM(6, 8) = 24.

How do I find the LCM in class 6?

Class 6 uses prime factorisation: write each number as a product of primes, take every prime at its highest power, multiply. LCM(12, 18) = 2² × 3² = 36.

How do I find the LCM in class 10?

Class 10 questions use HCF × LCM = product of two numbers. Find the HCF by prime factorisation or the Euclidean algorithm, then LCM = a × b ÷ HCF. LCM(96, 404) = 96 × 404 ÷ 4 = 9,696.

How do I teach the LCM to kids?

Start with skip counting: count in 4s and in 6s and circle the first number in both lists. Then show that the circled number, 12, is the smallest number both 4 and 6 divide into.

What grade teaches the LCM in the United States?

Grade 6, under Common Core standard 6.NS.B.4, with LCMs of numbers up to 12 and GCFs up to 100.

How do I check an LCM answer?

Divide the answer by each original number; every division must be exact. Then check that half the answer is not also divisible by every number.

Can I print these worksheets?

Yes. Use your browser's print command on this page; the navigation and answers are hidden in print, leaving the questions.

Are these questions the same every time?

Yes. Each set is fixed, so a class can use the same worksheet and the answers stay valid.

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