HCF And LCM

Question 1

What is HCF

Answer 1

Highest common factors

The highest number that both numbers are divisible by

Question 2

What are prime factors

Answer 2

The smallest numbers that a number is divisible by

Question 3

How can we find the prime factors

Answer 3

By using a factor tree we can split a number down into its prime factors

E.g 84

                             84 2.                                                42
                                    21.               2
                          3.      7 So the prime factors are 2×2×3×7 Or 2^2×3×7

Question 4

How can we find the HCF of two different numbers

Answer 4

First we find the prime factors of the number

E.g

28 = 2×2×7
42 = 2×3×7

Now see what prime factors can be seen in each number

In this case 2 and 7 are both there

Multiply these two numbers together to find the HCF
2×7=14

Question 5

What is LCM

Answer 5

The lowest common multiple between two numbers

This is the lowest whole number that both numbers can be multiplied into

Question 6

How is LCM between two numbers found

Answer 6

First find the prime factors of each number
E.g
12 = 2×2×3
18 = 2×3×3

Ensure the prime factors are placed in order

Both multiply by two so 1 of them is cancelled out
This is the same for three

(////) Represents the numbers being crossed out

12 = (2//) 2. (3///)
18 = 2 3. 3
This leaves us with 2×2×3×3
The LCM = 36

Question 7

What is The LCM of 15 and 45

Answer 7

20 = 4×5 = 2×2×5
45 = 8×5 = 3×3×5

2×2×5
3×3×5
Only the 5s are seen in both

2×2×3×3×5 = 180