HCF and LCM in real situations: Class 10 practice
Use HCF for 'greatest' size of equal groups or tiles; use LCM for 'least' common time or quantity. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- HCF and LCM
The idea behind hcf and lcm in real situations
Use HCF for 'greatest' size of equal groups or tiles; use LCM for 'least' common time or quantity. Check the answer divides (HCF) or is divisible by (LCM) all the given numbers.
Step-by-step method
- Identify greatest-equal-part (HCF) or least-common-multiple (LCM).
- Compute it.
- Check divisibility and answer in context.
Worked example 1 (Basic)
A room is 126 cm × 90 cm. What is the largest square tile that fits exactly?
- HCF(126, 90) = 18 cm
- Answer: 18 cm
Worked example 2 (Standard)
A room is 90 cm × 60 cm. What is the largest square tile that fits exactly, and how many are needed?
- HCF(90, 60) = 30 cm
- Tiles = (90/30) × (60/30) = 6
- Answer: 30 cm; 6 tiles
Worked example 3 (Challenge)
Three tankers hold 24, 36 and 40 litres. What is the largest container that measures each exactly?
- HCF(24, 36, 40) = 4
- Answer: 4 litres
Common mistakes and misconceptions
- Swapping HCF and LCM
- Answering with the number of groups instead of their size
Practice questions
- (Basic) A room is 36 cm × 66 cm. What is the largest square tile that fits exactly?
- (Basic) A room is 90 cm × 90 cm. What is the largest square tile that fits exactly?
- (Standard) A room is 75 cm × 100 cm. What is the largest square tile that fits exactly, and how many are needed?
- (Standard) A room is 32 cm × 64 cm. What is the largest square tile that fits exactly, and how many are needed?
- (Challenge) Three tankers hold 54, 66 and 72 litres. What is the largest container that measures each exactly?
- (Challenge) Three tankers hold 108, 180 and 126 litres. What is the largest container that measures each exactly?
Answer key with full working
- Q1: HCF(36, 66) = 6 cm → Answer: 6 cm
- Q2: HCF(90, 90) = 90 cm → Answer: 90 cm
- Q3: HCF(75, 100) = 25 cm → Tiles = (75/25) × (100/25) = 12 → Answer: 25 cm; 12 tiles
- Q4: HCF(32, 64) = 32 cm → Tiles = (32/32) × (64/32) = 2 → Answer: 32 cm; 2 tiles
- Q5: HCF(54, 66, 72) = 6 → Answer: 6 litres
- Q6: HCF(108, 180, 126) = 18 → Answer: 18 litres
Syllabus note
This skill is listed under "Real Numbers" for Class 10 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 in real situations in?
"Real Numbers", Class 10 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.