How does one find the highest common factor (HCF) and lowest common multiple (LCM) of 36 and 48?

  • Google+ icon
  • LinkedIn icon
  • 2605 views

36 and 48 are comprised of the following prime factors:

         36 = 2 x 2 x 3 x 3

         48 = 2 x 2 x 2 x 2 x 3

To find the highest common factor (HCF) we consider the prime factors that are the same for both 36 and 48:

         36 = 2 x 2 x 3 x 3

         48 = 2 x x 2 x 2 x 3

The prime factors that are the same are two 2s and one 3, so we multiply these to find the HCF:

         2 x 2 x 3 = 12.

So the HCF of 36 and 48 is 12.

To find the lowest common multiple (LCM) we consider which number consists of the most of each prime factor:

         36 = (2 x 2) x (3 x 3)

         48 = (2 x 2 x 2 x 2) x (3)

36 consists of the most 3s (two 3s); 48 consists of the most 2s (four 2s). So we multiply these two 3s and four 2s:

         (2 x 2 x 2 x 2) x (3 x 3) = 144

So the LCM of 36 and 48 is 144.

Anya K. A Level Maths tutor, GCSE Maths tutor, 13 plus  Maths tutor, ...

About the author

is an online GCSE Maths tutor with MyTutor studying at Bristol University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok