HCF and LCM word problems: Class 6 practice
Use the HCF when you split things into the largest equal groups or lengths. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- HCF and LCM by prime factorisation
The idea behind hcf and lcm word problems
Use the HCF when you split things into the largest equal groups or lengths. Use the LCM when you want the first time events happen together or the smallest number divisible by several numbers.
Step-by-step method
- Decide: largest equal part (HCF) or first common time/number (LCM)?
- Find HCF or LCM by prime factorisation.
- Answer in words with units.
Worked example 1 (Basic)
Ribbons of 120 cm and 105 cm are cut into equal pieces as long as possible with nothing left over. How long is each piece?
- HCF(120, 105) = 15
- Answer: 15 cm
Worked example 2 (Standard)
Two bells ring every 12 and 16 minutes. They ring together now. After how many minutes will they next ring together?
- 12 = 2 × 2 × 3, 16 = 2 × 2 × 2 × 2
- LCM = 48
- Answer: 48 minutes
Worked example 3 (Challenge)
Ribbons of 84 cm and 72 cm are cut into equal pieces as long as possible with nothing left over. How long is each piece and how many pieces are there?
- HCF(84, 72) = 12
- Pieces = 84/12 + 72/12 = 13
- Answer: 12 cm, 13 pieces
Common mistakes and misconceptions
- Using LCM for 'largest piece'
- Forgetting units in the answer
Practice questions
- (Basic) Ribbons of 54 cm and 99 cm are cut into equal pieces as long as possible with nothing left over. How long is each piece?
- (Basic) Ribbons of 35 cm and 25 cm are cut into equal pieces as long as possible with nothing left over. How long is each piece?
- (Standard) Two bells ring every 12 and 18 minutes. They ring together now. After how many minutes will they next ring together?
- (Standard) Two bells ring every 15 and 9 minutes. They ring together now. After how many minutes will they next ring together?
- (Challenge) Ribbons of 54 cm and 24 cm are cut into equal pieces as long as possible with nothing left over. How long is each piece and how many pieces are there?
- (Challenge) Ribbons of 45 cm and 150 cm are cut into equal pieces as long as possible with nothing left over. How long is each piece and how many pieces are there?
Answer key with full working
- Q1: HCF(54, 99) = 9 → Answer: 9 cm
- Q2: HCF(35, 25) = 5 → Answer: 5 cm
- Q3: 12 = 2 × 2 × 3, 18 = 2 × 3 × 3 → LCM = 36 → Answer: 36 minutes
- Q4: 15 = 3 × 5, 9 = 3 × 3 → LCM = 45 → Answer: 45 minutes
- Q5: HCF(54, 24) = 6 → Pieces = 54/6 + 24/6 = 13 → Answer: 6 cm, 13 pieces
- Q6: HCF(45, 150) = 15 → Pieces = 45/15 + 150/15 = 13 → Answer: 15 cm, 13 pieces
Syllabus note
This skill is listed under "Playing with Numbers" for Class 6 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is hcf and lcm word problems in?
"Playing with Numbers", Class 6 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.