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Complex LCM: Challenge & Extension

Mathematics

GCSE Foundation

11 questions

~22 mins

1 views0 downloads

About This Worksheet

A challenging worksheet focusing on finding the Least Common Multiple (LCM) of complex denominators to add fractions. Designed for GCSE Foundation students to develop procedural fluency and problem-solving skills.

Topics covered:

#Mathematics

#Number & Quantity

#Adding Fractions (Unlike Denominators)

#Complex LCM

#GCSE Foundation

Worksheet Preview

Full preview • 11 questions

Complex LCM: Challenge & Extension

Subject: MathematicsGrade: GCSE Foundation

Name:

Date:

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Untitled Worksheet

Grade GCSE Foundation

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.

Calculate the LCM of 8, 12, and 20.

[2 marks]

Add the fractions

\frac{3}{8}

and

\frac{5}{12}

. Show the common denominator process.

[3 marks]

Find the LCM of 18 and 24.

[2 marks]

Add

\frac{7}{18}

and

\frac{5}{24}

[3 marks]

Problem Solving & Reasoning

Answer all questions with detailed working.

A recipe requires

\frac{2}{3}

cup of sugar and

\frac{3}{4}

cup of honey. Find the total amount of sweet ingredients if you mix them together. Show all steps.

[4 marks]

A cyclist rides 5/8 km in one minute and 3/5 km in another minute. Find the least number of minutes needed to complete both rides in the same trip, assuming they are added. Show your working.

[4 marks]

Real-world Applications

Solve the following problems based on real-life contexts.

A factory produces 3/7 of a batch of widgets every hour, and another produces 4/9 of a batch every hour. How long will it take for both factories to complete exactly 1 batch working together? Show your working.

[4 marks]

Challenge & Extension

Attempt these more difficult problems to extend your understanding.

Add

\frac{5}{14}

\frac{3}{20}

, and

\frac{7}{18}

. Find the total sum in simplest form.

[4 marks]

A water tank is filled by two pipes. Pipe A fills

\frac{2}{5}

of the tank in 1 hour, while Pipe B fills

\frac{3}{8}

of the tank in 1 hour. How long will both pipes take to fill the tank together? Show detailed working.

[4 marks]

Mixed Review

Answer these questions that cover different aspects of Complex LCM.

Identify and correct the mistake: Adding

\frac{4}{9}

and

\frac{2}{3}

resulted in

\frac{6}{12}

[2 marks]

Compute the LCM of 15, 20, and 25.

[2 marks]

Answer Key

Fluency & Practice

Question 1: Calculate the LCM of 8, 12, and 20.

Answer: 120

Question 2: Add the fractions \( \frac{3}{8} \) and \( \frac{5}{12} \). Show the common denominator process.

Answer: Calculate LCM of 8 and 12 = 24. Convert: \( \frac{3}{8} = \frac{9}{24} \), \( \frac{5}{12} = \frac{10}{24} \). Sum: \( \frac{19}{24} \).

Question 3: Find the LCM of 18 and 24.

Answer: 72

Question 4: Add \( \frac{7}{18} \) and \( \frac{5}{24} \).

Answer: LCM of 18 and 24 = 72. Convert: \( \frac{7}{18} = \frac{28}{72} \), \( \frac{5}{24} = \frac{15}{72} \). Sum: \( \frac{43}{72} \).

Problem Solving & Reasoning

Question 1: A recipe requires \( \frac{2}{3} \) cup of sugar and \( \frac{3}{4} \) cup of honey. Find the total amount of sweet ingredients if you mix them together. Show all steps.

Answer: LCM of 3 and 4 = 12. \( \frac{2}{3} = \frac{8}{12} \), \( \frac{3}{4} = \frac{9}{12} \). Total: \( \frac{17}{12} \) cups.

Question 2: A cyclist rides 5/8 km in one minute and 3/5 km in another minute. Find the least number of minutes needed to complete both rides in the same trip, assuming they are added. Show your working.

Answer: LCM of 8 and 5 = 40. Convert: \( \frac{5}{8} = \frac{25}{40} \), \( \frac{3}{5} = \frac{24}{40} \). Total per cycle: \( \frac{49}{40} \) km. Minimum minutes for whole unit: 40, total distance: 49 km.

Real-world Applications

Question 1: A factory produces 3/7 of a batch of widgets every hour, and another produces 4/9 of a batch every hour. How long will it take for both factories to complete exactly 1 batch working together? Show your working.

Answer: LCM of 7 and 9 = 63. Factory 1: \( \frac{3}{7} = \frac{27}{63} \), Factory 2: \( \frac{4}{9} = \frac{28}{63} \). Combined rate: \( \frac{55}{63} \) per hour. Time: \( \frac{63}{55} \) hours (~1.15 hours).

Challenge & Extension

Question 1: Add \( \frac{5}{14} \), \( \frac{3}{20} \), and \( \frac{7}{18} \). Find the total sum in simplest form.

Answer: LCM of 14, 20, 18 = 1260. Convert: \( \frac{5}{14} = \frac{450}{1260} \), \( \frac{3}{20} = \frac{189}{1260} \), \( \frac{7}{18} = \frac{490}{1260} \). Sum: \( \frac{1129}{1260} \).

Question 2: A water tank is filled by two pipes. Pipe A fills \( \frac{2}{5} \) of the tank in 1 hour, while Pipe B fills \( \frac{3}{8} \) of the tank in 1 hour. How long will both pipes take to fill the tank together? Show detailed working.

Answer: LCM of 5 and 8 = 40. Pipe A: \( \frac{2}{5} = \frac{16}{40} \), Pipe B: \( \frac{3}{8} = \frac{15}{40} \). Combined rate: \( \frac{31}{40} \) per hour. Time: \( \frac{40}{31} \) hours (~1.29 hours).

Mixed Review

Question 1: Identify and correct the mistake: Adding \( \frac{4}{9} \) and \( \frac{2}{3} \) resulted in \( \frac{6}{12} \).

Answer: Incorrect sum. Correct LCM of 9 and 3 is 9. \( \frac{2}{3} = \frac{6}{9} \). Sum: \( \frac{4}{9} + \frac{6}{9} = \frac{10}{9} \).

Question 2: Compute the LCM of 15, 20, and 25.

Answer: 300

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Details

Created: 1/1/2026
Updated: 1/1/2026
Type: worksheet

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Complex LCM: Challenge & Extension

About This Worksheet

Topics covered:

Worksheet Preview

Complex LCM: Challenge & Extension

Untitled Worksheet

Fluency & Practice

Problem Solving & Reasoning

Real-world Applications

Challenge & Extension

Mixed Review

Quick Actions

What is Remix?

Details

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