1.1.3 Highest common factors(HCF) & Lowestcommon multiples(LCM)

HIGHEST COMMON FACTOR (HCF) AND LOWEST COMMON MULTIPLE (LCM)

Learning Outcomes

Find HCF and LCM of given numbers using listing or prime factorization.

Apply HCF and LCM in real-life problems.

Lesson Notes

Finding HCF

Listing Method: List factors of each number and find the largest common one.

Prime Factorization Method: Express numbers as a product of primes and take the lowest powers of common primes.

Finding LCM

Listing Method: List multiples of each number and find the smallest common one.

Prime Factorization Method: Take the highest powers of all primes.

Worked Examples

Example 1: HCF

Find HCF of 18 and 24.

18 = 2 × 3 × 3 = 2 × 3²

24 = 2³ × 3

Common factors = 2 × 3 = 6

HCF = 6

Example 2: LCM

Find LCM of 6 and 8.

6 = 2 × 3

8 = 2³

LCM = 2³ × 3 = 24

LCM = 24

Example 3: Real-Life Application

Two traffic lights flash every 30 seconds and 45 seconds respectively.

After how many seconds will they flash together?

LCM(30, 45) = 90 seconds

Answer: After 90 seconds.

Exercise 3

1. Find HCF(20, 30)

2. Find LCM(9, 12)

3. Find HCF and LCM of 15 and 25

4. Three bells ring every 8, 12, and 16 minutes. When will they ring together again?