LCM and HCF of three numbers: Class 6 practice
Extend prime factorisation to three numbers: HCF uses primes common to all three (lowest power), LCM uses every prime at its highest power.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- HCF and LCM of two numbers
The idea behind lcm and hcf of three numbers
Extend prime factorisation to three numbers: HCF uses primes common to all three (lowest power), LCM uses every prime at its highest power.
Step-by-step method
- Prime factorise each number.
- HCF: common primes at lowest power.
- LCM: all primes at highest power.
Worked example 1 (Basic)
Find the HCF of 5, 26 and 22.
- HCF(5, 26) = 1
- HCF(1, 22) = 1
- Answer: 1
Worked example 2 (Standard)
Find the LCM of 16, 10 and 12.
- LCM(16, 10) = 80
- LCM(80, 12) = 240
- Answer: 240
Worked example 3 (Challenge)
Find the LCM of 5, 14 and 4. Three bells ring at these intervals in seconds; when do they next ring together?
- LCM(5, 14) = 70
- LCM(70, 4) = 140
- Answer: 140 seconds
Common mistakes and misconceptions
- Multiplying all three numbers for the LCM
- Using a prime that isn't common to all three for the HCF
Practice questions
- (Basic) Find the HCF of 13, 9 and 9.
- (Basic) Find the HCF of 28, 12 and 17.
- (Standard) Find the LCM of 18, 12 and 10.
- (Standard) Find the LCM of 9, 27 and 18.
- (Challenge) Find the LCM of 4, 4 and 9. Three bells ring at these intervals in seconds; when do they next ring together?
- (Challenge) Find the LCM of 23, 13 and 19. Three bells ring at these intervals in seconds; when do they next ring together?
Answer key with full working
- Q1: HCF(13, 9) = 1 → HCF(1, 9) = 1 → Answer: 1
- Q2: HCF(28, 12) = 4 → HCF(4, 17) = 1 → Answer: 1
- Q3: LCM(18, 12) = 36 → LCM(36, 10) = 180 → Answer: 180
- Q4: LCM(9, 27) = 27 → LCM(27, 18) = 54 → Answer: 54
- Q5: LCM(4, 4) = 4 → LCM(4, 9) = 36 → Answer: 36 seconds
- Q6: LCM(23, 13) = 299 → LCM(299, 19) = 5681 → Answer: 5681 seconds
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 lcm and hcf of three numbers 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.