Highest Common Factor, Least Common Multiple

Highest Common Factor (HCF)

Question
What is the HCF of 24 and 36?

To answer this question, first list the factors of 24 and 36. Remember, factors are the numbers that go into 24 and 36 (the numbers that will divide 24 and 36 exactly).

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Then the Highest Common Factor will be the highest (largest) factor that appears in both lists (common).

Solution
HCF = 12



Least Common Multiple (LCM)

Question
What is the LCM of 10 and 15?

To answer this question, first list the multiples of 10 and 15. Remember, multiples are the numbers that appear in the timestables of 10 and 15.

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, ...

Then the Least Common Multiple will be the least (lowest) multiple that appears in both lists (common).

Solution
LCM = 30

Remember: Learn the definitions of factors and multiples so that you don't confuse yourself!

Exam Questions
Have a go at these questions:

1. What is the LCM of 24 and 36?

2. What is the HCF of 15 and 45?

3. I am thinking of two numbers.
Their LCM is 45, and their HCF is 3.
What could the two numbers be?
Hint: List the factors of 45 and the multiples of 3 to help you find possible solutions.

Send your answers to mathshints@gmail.com
(Solutions will be posted soon!)