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Finding Common Ground – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 11. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Common factors and common multiples solve sharing and timing problems. HCF and LCM can be found by listing or by prime factorisation.

HCF (highest common factor)

Largest number that divides all given numbers.
Prime factorisation: take common primes with the smallest powers.
Used for: largest equal pieces, biggest tile that fits a floor exactly.

LCM (lowest common multiple)

Smallest number divisible by all given numbers.
Prime factorisation: take all primes with the greatest powers.
Used for: when events happen together again (bells, buses, lights).

Key terms

Common factor: a number that divides two or more numbers
Co-prime numbers: numbers whose HCF is 1
HCF: highest common factor, the largest number that divides all the given numbers

Formulas

HCF × LCM = product of two numbers
LCM of co-primes = their product

Important questions with answers

Find the HCF of 18 and 27.2 marks

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. HCF = 9.

Are 15 and 28 co-prime? Explain.3 marks

Yes. 15 = 3 × 5 and 28 = 2² × 7 have no common factor other than 1.

Two ropes are 64 m and 80 m long. They are to be cut into equal pieces of the greatest possible length. Find the length of each piece and the total number of pieces. Also find the LCM of 64 and 80 and check that HCF × LCM = 64 × 80.5 marks

HCF: 64 = 2⁶, 80 = 2⁴ × 5, so HCF = 2⁴ = 16 m. Pieces = 64/16 + 80/16 = 4 + 5 = 9. LCM = 2⁶ × 5 = 320. HCF × LCM = 16 × 320 = 5120 = 64 × 80 ✓.

Quick revision

HCF ≤ smallest number ≤ LCM.
Co-primes have HCF 1.
Product rule works for two numbers.

Exam tips

"Largest / greatest / maximum size" usually means HCF; "next time together / smallest" means LCM.
The HCF is never larger than the smallest number.

Practice MCQs

HCF of 12 and 16 is
1. 2
2. 4
3. 8
4. 48
Show answer
Answer: (b) 4. Largest common factor.
LCM of 4 and 5 is
1. 9
2. 1
3. 40
4. 20
Show answer
Answer: (d) 20. Co-primes: product.
Two bells ring every 6 and 8 minutes. If they ring together now, they will ring together again after
1. 14 min
2. 24 min
3. 48 min
4. 2 min
Show answer
Answer: (b) 24 min. LCM.
The largest length that can measure 24 m and 36 m exactly is
1. 6 m
2. 12 m
3. 72 m
4. 4 m
Show answer
Answer: (b) 12 m. HCF.
HCF of 24 and 36 is
1. 6
2. 4
3. 72
4. 12
Show answer
Answer: (d) 12. 2² × 3.
HCF of two numbers is 6 and their product is 216. Their LCM is
1. 1296
2. 18
3. 12
4. 36
Show answer
Answer: (d) 36. 216 ÷ 6.
Which pair is co-prime?
1. 12, 18
2. 9, 27
3. 14, 21
4. 15, 28
Show answer
Answer: (d) 15, 28. Common factor only 1.
The largest tile size that exactly covers a floor 480 cm × 360 cm is
1. 60 cm
2. 240 cm
3. 40 cm
4. 120 cm
Show answer
Answer: (d) 120 cm. HCF of 480 and 360.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.