HCF and LCM word problems

2026-11-09Numbers & Estimation Mr Ng

Choose HCF for greatest shared size and LCM for repeating cycles.

Key formulas

\text{HCF for sharing}

\text{LCM for repeating events}

What this lesson covers

This lesson builds Secondary 2–3 skill in HCF LCM applications. Read the key formulas, study the worked example, then attempt the written practice and the four-question MCQ review.

Method

Write every step. Name the rule you use (HCF LCM applications) before substituting numbers. Keep units and signs visible until the final sentence.

Common mistakes

Students often rush the sign, use the wrong percentage base, or cancel terms instead of factors. Pause after each line and ask whether the step is reversible.

Exam habit

Underline the question verb (simplify, solve, factorise, find). Box the final answer and, where sensible, substitute back for a quick check.

Worked example

Worked example — HCF LCM applications

Problem. Apply the method for HCF LCM applications with the numbers 5 and 6.

Solution. Identify the rule for HCF LCM applications. Substitute 5 and 6 carefully with signs in brackets if needed. Complete each operation on a new line. State the final answer clearly and check by reversing one step.

Review quiz

1 / 4

Warm-up on HCF LCM applications: what is 3+4?

Practice questions

Practice 1 on HCF LCM applications: compute with the value 17.
Practice 2 on HCF LCM applications: change the numbers and repeat the same method.
Practice 3 on HCF LCM applications: write one sentence explaining the key rule.
Practice 4 on HCF LCM applications: invent a similar exam-style question and solve it.

Study notes

What is the main idea of HCF LCM applications?

Apply the stated formula or rule with clear steps, then check by reversing or substituting.

How should I revise this topic?

Cover the worked example, redo the practice without notes, then complete the MCQ set and log any wrong options.