JSS1 First Term Mathematics Lesson Note – LCM and HCF of Whole Numbers

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WEEK – 4

TOPIC:  LCM and HCF of whole numbers:

CONTENTS:

• Rules of divisibility
• Definitions: Even, odd, Prime and composite numbers.
• Factors, Multiples and Index form.
• Expressing Numbers as product of Prime Factors.
• Common factors and the Highest Common Factor (H.C.F) of whole numbers
• Least Common Multiple (L.C.M) of whole numbers.
• Quantitative reasoning.

Rules of Divisibility

There are some simple rules of divisibility which enable us to find out whether a certain number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11.

Any whole number is exactly divisible by

2 if its last digit is even or zero

3 if the sum of its digits is divisible by 3

4 if its last two digits form a number divisible by 4

5 if its last digits is 5 or 0

6 if its last digit is even and the sum of its digits is divisible by 3

8 if its last three digits form a number divisible by 8

9 if the sum of its digits is divisible by 9

10 if its last digit is 0

11 if the difference between the sum of the digits in the odd places and the sum of the digits in the even places is divisible by 11, or the difference is zero.

CLASS ACTIVITY

1. Using the rules of divisibility, find out which of the following numbers are divisible by
2. a) 2 b) 5 c) 4
3. i) 136 ii) 4 881 iii) 372 iv) 62, 784 v) 1010
4. Which of the following numbers are divisible by a) 3 and 9 b) 4 and 5?
5. a) 637 245 b) 134 721 c) 10140.

DEFINITIONS

EVEN NUMBERS: Even numbers are numbers that when divided by two has no remainder. All numbers that end in 0, 2, 4, 6, and 8 are even. Examples include: 34, 86, 26890, etc.

ODD NUMBERS: These set of numbers has a remainder of one when it is divided by 2. All numbers that end in 1, 3, 5, 7 and 9 are odd numbers. Examples are 81, 1247, 30096, etc.

COMPOSITE NUMBERS: These are numbers that are not prime numbers. They have factors other than 1 and the number itself. All even numbers except 2 are composite numbers.

FACTORS, MULTIPLES & THEIR RELATIONSHIP

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