Highest Common Factor (HCF) and Lowest Common Factor (LCF) – JSS2 Mathematics Lesson Note (First Term)

The HCF of numbers is found by writing each number as a product of prime factors and multiplying the factors they share. The LCM is found by the division method or by prime factors. A square is a number multiplied by itself, and a square root is the number that gives the original when multiplied by itself.

Behavioural objectives

By the end of the lesson, students should be able to:

• find the LCM (lowest common multiple) of two numbers using the division method and the prime factor method;
• find the HCF (highest common factor) of two numbers using prime factors;
• find the square of a number;
• find the square root of a number using the prime factor method and the factor pairs method.

How do you find the LCM of two numbers?

There are two methods. In Method 1 (division method), divide the numbers by prime numbers until both reach 1, then multiply the divisors. In Method 2, write each number as a product of prime factors, then multiply the factors, using each one as many times as it appears in the number where it appears most.

Example 1: Find the LCM of 18 and 24

Method 1: Division method

LCM = 2 × 2 × 2 × 3 × 3 = 72

Method 2: Prime factors

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

LCM = 2 × 2 × 2 × 3 × 3 = 72

Example 2: Find the LCM of 72 and 90

Method 1: Division method

LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360

Method 2: Prime factors

72 = 2 × 2 × 2 × 3 × 3

90 = 2 × 3 × 3 × 5

LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360

How do you find the HCF of two numbers?

Write each number as a product of prime factors and pick the common ones. Multiply the common factors to get the HCF.

Example 3: Find the HCF of 72 and 96

72 = 2 × 2 × 2 × 3 × 3

96 = 2 × 2 × 2 × 2 × 2 × 3

The common factors are 2 × 2 × 2 × 3.

HCF = 2 × 2 × 2 × 3 = 24

What is a square?

A square is the product of two equal terms, for example N × N = N².

Example: Find the square of 14 and 21

1. 14 × 14 = 196
2. 21 × 21 = 441

What is a square root?

A square root is a number that, when multiplied by itself, equals a given number.

Example: Find the square root of 144

Method 1: Prime factor method

144 = (2 × 2) × (2 × 2) × (3 × 3)

Take one number from each pair: 2 × 2 × 3 = 12. The square root of 144 is 12.

Method 2: Factor pairs method

• 144 = 1 × 144
• 144 = 2 × 72
• 144 = 3 × 48
• 144 = 4 × 36
• 144 = 6 × 24
• 144 = 8 × 18
• 144 = 9 × 16
• 144 = 12 × 12

The two factors in the last pair are equal, so the square root of 144 is 12.

Evaluation

1. Find the LCM of 12 and 18 using the division method.
2. Find the LCM of 20 and 30 using prime factors.
3. Find the HCF of 48 and 72.
4. Find the square of 15.
5. Find the square root of 196 using the prime factor method.

Assignment

1. Find the LCM of 36 and 48.
2. Find the HCF of 60 and 84.
3. Find the square of 17.
4. Find the square root of 225 using the factor pairs method.