NCERT Ganita Prakash, Class 7, textbook pages 47–66 (Part 2)

How to teach Class 7 Maths Part 2 Chapter 3, Finding Common Ground, at home

HCF and LCM, taught with things you already have at home: a 20-minute activity, a game for the week, a 5-day plan and the mistakes to watch for.

24 = 2³ × 3 36 = 2² × 3²HCF = 2² × 3 = 12LCM = 2³ × 3² = 72

NCERT Class 7 Maths Part 2 Chapter 3 Finding Common Ground: what it teaches

Cutting the biggest equal tiles for a room, or finding when two events happen together, uses the highest common factor and lowest common multiple. Your child finds HCF and LCM by listing and by prime factorisation, and solves real problems.

Why it matters later. HCF and LCM are used in fractions, ratios and algebraic factorisation later.

See it: this chapter in pictures

24: 1,2,3,4,6,8,12,2436: 1,2,3,4,6,9,12,18,36HCF = 12
The biggest shared factor.
bells: every 12 and 18 minLCM(12, 18)= 36 minutes
Events that repeat: LCM.
HCF × LCM = product12 × 72 = 864= 24 × 36 ✓
A handy check.

You need

  • squared paper
  • a 1–100 chart
  • coloured pencils

Tonight’s 20 minutes

  1. List factors of 24 and 36. Find the highest common one (12).
  2. On the 1–100 chart, mark multiples of 4 and 6. First common one? (12)
  3. Find HCF and LCM of 48 and 180 by prime factorisation.
  4. Problem: bells ring every 12 and 18 minutes. When together again?

Words to use

  • factor
  • multiple
  • HCF
  • LCM
  • prime factorisation
  • common

Watch for

  • Mixing up HCF and LCM. HCF is at most the smaller number; LCM is at least the larger.
  • Missing a prime factor. Check the factorisation by multiplying back.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouBells ring every 12 and 18 minutes. HCF or LCM?

Your childLCM: 36 minutes.

A game for this week: Tile or bells?

  1. Read a problem card.
  2. Decide: is it an HCF or LCM problem?
  3. Solve it.
  4. Points for correct choice and answer.

A 5-day plan, 20 minutes a day

  1. Day 1Factors and HCF.
  2. Day 2Multiples and LCM.
  3. Day 3Prime factorisation method.
  4. Day 4Word problems.
  5. Day 5Tile or bells? game.

Everyday moments to practise

  • Tiling a floor with biggest tiles.
  • Bus timetables.
  • Packing equal gift bags.
  • Gear teeth.

Quick check

Ask these at the end of the week. Tap to see the answer.

HCF of 24 and 36?

12.

LCM of 4 and 6?

12.

Bells every 12 and 18 minutes ring together every?

36 minutes.

Ready for the next chapter when your child…

  • Finds HCF and LCM.
  • Uses prime factorisation.
  • Chooses HCF or LCM for problems.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Prakash (Class 7). See the full Class 7 parent guide for every chapter.

Questions parents ask

What is HCF?

The highest common factor of numbers.

What is LCM?

The lowest common multiple of numbers.

Relation between HCF and LCM of two numbers?

HCF × LCM = product of the two numbers.