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Mathable Smart Lab

CLASS VII • NUMBER SENSETopic: HCF & LCM

Finding Common Ground

Explore highest common factor, lowest common multiple, tiling, grouping, meeting cycles, and prime factorization.

Fact Sheet: HCF and LCM

HCF means Highest Common Factor: the largest number that divides two or more numbers exactly.

LCM means Lowest Common Multiple: the smallest number that is a multiple of two or more numbers.

Use HCF when you want the biggest equal group, biggest square tile, or largest common size.
Use LCM when events repeat together, bells ring together, or cycles meet again.
Room Tile Example: For a 12 ft by 16 ft room, the largest square tile has side HCF(12,16) = 4 ft.

Formula Hub

Factors

Numbers that divide a number exactly.

Factors of 12: 1, 2, 3, 4, 6, 12.

Common Factors

Factors shared by two or more numbers.

Common factors of 12 and 16: 1, 2, 4.

HCF

Largest common factor.

HCF(12,16) = 4.

Multiples

Numbers in a times table.

Multiples of 6: 6, 12, 18, 24...

LCM

Smallest common multiple.

LCM(6,8) = 24.

HCF × LCM Rule

For two numbers: product = HCF × LCM.

12 × 16 = 4 × 48.

Online Lab: Common Ground Finder

Score: 0Current Streak: 🔥 0Badge: Factor Finder


Activity Zone

🧮 HCF & LCM Calculator

🧱 Tile the Room

Find the largest square tile for a rectangular room.

🔍 Factor Explorer

🔁 Multiple Race

Find the first common multiple.

⚖️ HCF or LCM?

Worksheet Generator

Generate HCF, LCM, tiling, grouping, and repeating-cycle problems.



Real-World Use

Tiling: Use HCF to find the largest square tile with no leftovers.
Grouping: Use HCF to make the largest equal groups.
Schedules: Use LCM to find when repeating events happen together.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

  • List factors and multiples of numbers.
  • Find common factors and common multiples.
  • Calculate HCF and LCM using listing and prime-factor thinking.
  • Choose HCF or LCM based on real-life context.
  • Solve tiling, grouping, and schedule problems.

Exit Ticket Prompts

  • Why is HCF used for the largest square tile?
  • Find HCF and LCM of 12 and 18.
  • Two bells ring every 6 and 8 minutes. When will they ring together?