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Class 7 Finding Common Ground: cheat sheet
CBSE Mathematics. Prime factorisation, highest common factor (HCF) and lowest common multiple (LCM), and the problems each one solves.
Key ideas
- Every number above 1 is a product of primes in only one way, e.g. 600 = 2³ × 3 × 5².
- HCF: multiply the lowest power of each prime that is common to all the numbers.
- LCM: multiply the highest power of every prime that appears in any of the numbers.
- Co-prime numbers have HCF 1, so their LCM is their product.
- HCF answers “largest equal piece or tile”; LCM answers “when do they next meet or ring together”.
Remember
| Two numbers | HCF × LCM = product of the numbers |
| Example | 675 = 3³ × 5², 600 = 2³ × 3 × 5²: HCF = 3 × 5² = 75, LCM = 2³ × 3³ × 5² = 5400 |
| Co-prime | HCF = 1, LCM = a × b |
Watch out
- Using the highest powers for the HCF.
- Applying HCF × LCM = product to three numbers.
- Choosing the LCM for a tiling problem (it needs the HCF).
Worked example
Write 675 and 600 in prime-power form, then find their HCF and LCM.
Working: HCF: lowest power of each common prime; LCM: highest power of every prime
Answer: 3³ × 5², 2³ × 3 × 5²; HCF 75, LCM 5400
Practise Finding Common Ground
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