Revision Notes for Class 7 Maths Chapter 11: Finding Common Ground

Quick revision notes summarizing all key concepts from Class 7 Maths Chapter 11 “Finding Common Ground”. These Class 7 Mathematics Chapter 11 notes are ideal for quick revision just before exams.

• HCF (Highest Common Factor): the largest number that divides two or more given numbers exactly.
• LCM (Least Common Multiple): the smallest number that is a multiple of two or more given numbers.
• Prime factorisation method for HCF: take the product of the common prime factors, each at its lowest power.
• Prime factorisation method for LCM: take the product of all prime factors involved (common and uncommon), each at its highest power.
• The division (repeated division) method is a faster way to find the HCF of larger numbers without full prime factorisation.
• Two consecutive numbers are always co-prime (HCF = 1); the HCF of two consecutive even numbers is always 2.
• Co-prime numbers: HCF = 1; for co-prime numbers, LCM always equals their product.
• Key relationship: HCF × LCM = product of the two numbers (holds only for exactly two numbers).
• Use LCM for “smallest number divisible by several numbers” problems — e.g. bells tolling together, events repeating at fixed intervals, or finding a smallest number leaving a given remainder.
• Use HCF for “largest equal-sized grouping” problems — e.g. tiling, cutting ropes into equal pieces, or packing goods into equal-weight bags with none left over.

See also: NCERT Solutions for Class 7 Maths Chapter 11

Practice more: Extra Questions for Class 7 Maths Chapter 11

For the full chapter, see the Class 7 Maths Part 2 book page and the Class 7 Maths Formulas Handbook.

Written by Satish

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