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

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.

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