Lowest Common Multiple (LCM) & Highest Common Factor (HCF)

These are fairly easy, so don’t get caught out by them in the exam!

What Is A Lowest Common Multiple (LCM)?

The lowest common multiple is just the smallest number that will divide by all the numbers in the question. In order to find what it is simply write out the multiples of each till you find one that is common to both. So the lowest common multiple of 8 and 14 is 56.
Sometimes people also call it a “least common multiple”, though that doesn’t strictly make logical sense.

Questions about LCM usually come connected to anther topic though:

What Is The Highest Common Factor (HCF)?

This just means the biggest number that will divide into all the numbers in the question. So the highest common factor of 24, 60 and 72 is 12.
highest common factorsexample questionsHere’s a bunch of example questions. To reveal the answer click on the “answer” tab.

What is the lowest common multiple of 9 and 12?
36. This should be fairly straight forward to answer if you follow the steps above.
What is the LCM of 5 and 10?
10
What is the highest common factor of 12 and 18?
8. Remember to write out all the factors of both numbers and then pick the highest one that occurs in both sets of numbers.
What is the HCF of 18, 36 and 48?
6.

The method remains the same no matter how many numbers there are in the question. So here you would write out all the factors of each sets of numbers:

Factors of 18 are 1, 2, 3, 6, 9, 18.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The numbers that appear in every one of these sets are 1, 2, 3, 6 – and the highest of these is 6.