HCF and LCM by prime factorisation: Class 6 practice

What you should know first

• Divisibility rules for 2, 3, 5
• Recognising prime numbers

The idea behind hcf and lcm by prime factorisation

The HCF is the product of the prime factors two numbers share; the LCM uses every prime factor the larger number of times it appears. For any two numbers, HCF × LCM = product of the numbers.

Step-by-step method

1. Write each number as a product of primes.
2. HCF: multiply the common primes (lowest power).
3. LCM: multiply every prime at its highest power.
4. Check: HCF × LCM should equal the product of the two numbers.

Worked example 1 (Basic)

Find the HCF and LCM of 15 and 20.

1. 15 = 3 × 5
2. 20 = 2 × 2 × 5
3. Common part: HCF = 5
4. LCM = (15 × 20) ÷ 5 = 60
5. Answer: HCF = 5, LCM = 60

Worked example 2 (Standard)

Find the HCF and LCM of 72 and 84.

1. 72 = 2 × 2 × 2 × 3 × 3
2. 84 = 2 × 2 × 3 × 7
3. Common part: HCF = 12
4. LCM = (72 × 84) ÷ 12 = 504
5. Answer: HCF = 12, LCM = 504

Worked example 3 (Challenge)

Find the HCF and LCM of 90 and 108.

1. 90 = 2 × 3 × 3 × 5
2. 108 = 2 × 2 × 3 × 3 × 3
3. Common part: HCF = 18
4. LCM = (90 × 108) ÷ 18 = 540
5. Answer: HCF = 18, LCM = 540

Common mistakes and misconceptions

• Adding factors instead of multiplying them
• Using the HCF where a question about 'smallest common multiple' needs the LCM

Practice questions

1. (Basic) Find the HCF and LCM of 6 and 21.
2. (Basic) Find the HCF and LCM of 25 and 10.
3. (Standard) Find the HCF and LCM of 16 and 40.
4. (Standard) Find the HCF and LCM of 32 and 40.
5. (Challenge) Find the HCF and LCM of 126 and 162.
6. (Challenge) Find the HCF and LCM of 105 and 120.

Answer key with full working

• Q1: 6 = 2 × 3 → 21 = 3 × 7 → Common part: HCF = 3 → LCM = (6 × 21) ÷ 3 = 42 → Answer: HCF = 3, LCM = 42
• Q2: 25 = 5 × 5 → 10 = 2 × 5 → Common part: HCF = 5 → LCM = (25 × 10) ÷ 5 = 50 → Answer: HCF = 5, LCM = 50
• Q3: 16 = 2 × 2 × 2 × 2 → 40 = 2 × 2 × 2 × 5 → Common part: HCF = 8 → LCM = (16 × 40) ÷ 8 = 80 → Answer: HCF = 8, LCM = 80
• Q4: 32 = 2 × 2 × 2 × 2 × 2 → 40 = 2 × 2 × 2 × 5 → Common part: HCF = 8 → LCM = (32 × 40) ÷ 8 = 160 → Answer: HCF = 8, LCM = 160
• Q5: 126 = 2 × 3 × 3 × 7 → 162 = 2 × 3 × 3 × 3 × 3 → Common part: HCF = 18 → LCM = (126 × 162) ÷ 18 = 1134 → Answer: HCF = 18, LCM = 1134
• Q6: 105 = 3 × 5 × 7 → 120 = 2 × 2 × 2 × 3 × 5 → Common part: HCF = 15 → LCM = (105 × 120) ÷ 15 = 840 → Answer: HCF = 15, LCM = 840

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

• Prime and composite numbers
• Divisibility rules for 3, 4, 9 and 11
• HCF and LCM word problems
• LCM and HCF of three numbers
• Adding and subtracting unlike fractions
• Unitary method word problems
• Perimeter and area of rectangles
• Indian and international place value
• All Class 6 practice

Frequently asked questions

Which chapter is hcf and lcm by prime factorisation 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.