Finding of common multiples and common factors (LCM and HCF)

LCM: Lowest Common Multiple.

HCF: Highest Common Factor.

Examples on HCF:
1.  Find the HCF of 6 and 16

Factors of 6 = {1, 2, 3, 6}
Factors of 16 = {1, 2, 4, 8, 16}
Common factors = {1, 2}
The greatest is 2 so HCF of 6 and 16 is 2

2.  Find the HCF of 24 and 54

Factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24}
Factors of 54 = {1, 2, 3, 6, 9, 18,27,54}
Common factors = {1, 2, 3, 6}
The greatest is  6 so HCF of 24 and 54 is 6

Exercises on HCF

1. Find the HCF between the following;
a. 2 and 6
b. 12 and 36
c. 54 and 62
Bonus: 72 and 108

Examples on LCM

1. Find the LCM of 4 and 6

Multiples of 4 = {4, 8, 12, 16, 20, 24, ...}
Multiples of 6 = {6, 12, 18, 24, 30, 36, ...}

We might have too many multiples, but we need the lowest. A few of them are {12, 24, ...}
The lowest multiple is 12.

2. Find the LCM of 5 and 7

Multiples of 5 = {5, 10, 15, 20, 25, 30, 35, ...}
Multiples of 7 = {7, 14, 21, 28, 35, ...}

The multiples are still numerous but we need the lowest. Check if 70 is a multiple too.
The lowest multiple is 35.

Exercises on LCM:
[Try this ones, if you encounter any problem, refer back to the examples. Good Luck!!!]
1.  Find the LCM of the following;
a. 2 and 8
b. 3 and 5
c. 13 and 15
d. 26 and 17