GCD, LCM and Applications

• the core idea behind GCD, LCM and Applications and how it fits inside Number Theory Basics.
• Mastering GCD, LCM and Applications sharpens your problem-solving toolkit for olympiad-style questions beyond routine NCERT problems.
• A clear worked example you can copy into your notebook.

1. GCD (greatest common divisor) is the largest number dividing two or more integers.
2. LCM (least common multiple) is the smallest positive number divisible by all the given integers.
3. Key identity: GCD(a,b) x LCM(a,b) = a x b.
4. The Euclidean algorithm finds GCD efficiently via repeated division with remainder.

Find the GCD of 1071 and 462 using the Euclidean algorithm.

Step 1 — 1071 = 462 x 2 + 147
Step 2 — 462 = 147 x 3 + 21
Step 3 — 147 = 21 x 7 + 0
Step 4 — the last non-zero remainder is the GCD: 21

• Confusing GCD and LCM — GCD is always ≤ the smaller number, LCM is always ≥ the larger number.
• Forgetting that GCD(a,b) x LCM(a,b) = a x b only works for exactly two numbers.
• Making arithmetic slips during the repeated division steps of the Euclidean algorithm.

• Find GCD(84,126) and LCM(84,126).
• Two ropes measure 45m and 75m — find the greatest length that can measure both exactly.
• Find the smallest number that leaves remainder 3 when divided by 6, 8, or 10.

Open the Practice tab for graded questions on GCD, LCM and Applications.

• Use the platform-native live simulation or PhET-style tool for this topic (number line, Venn, physics playground, molecule builder, sensor dashboard, etc.).
• Mirror / body / home activity: physically do the concept (count objects, measure, role-play) and photograph or describe for portfolio.
• Voice or text reflection with AI Mentor: explain the concept to a younger student or family member.

• "Explain this concept to a Class 6 student using one real example from an Indian home, school, market, or festival."
• "What is one common mistake students make here, and how would you catch yourself making it?"
• Stretch: "How does this connect to coding, robotics, money, health, environment, or a future career?"

• Complete the core practice + one extension activity (photo, table, short reflection, or mini-project) for base XP + topic badge.
• 5-7 day streak or family discussion note = multiplier + visible artifact in parent/principal dashboard.
• Best real-world application stories (anonymised) featured on class or national leaderboard.

• One hands-on project or measurement using the Drishti kit or household items that makes the concept physical.
• Direct link to at least one Future Skill track (Money Management, Green Tech, Cyber Defenders, Micro-Entrepreneurship, AI Mastery, Sustainable Living, Personality Development).
• Coding extension where relevant (simple script, simulation, or data logging).

This material emphasises experiential "learning by doing", competency (apply/create/analyse), vocational exposure, critical thinking, and multidisciplinary connections. Designed to feed live worlds, AI Mentor (with memory), gamification, robotics, parent analytics, and future skills — not just exam prep.

Portfolio Evidence Idea: Your photo/table/reflection/project + one sentence on "How this helps me in real life or a possible future path."

Open the Practice tab for aligned questions (easy/medium/hard + case-based) with full AI scaffolding.

See curriculum for cross-links and the full future-skills/robotics chapters.