Question

3. (i) Find the HCF and LCM of 120 and 126.

(ii) Show that the product of the HCF and LCM of 120 and 126 is equal to the
product of 120 and 126. By looking at their prime factorisation,

(iii) Can you generalise the result in (ii) for any two numbers?

(iv) Can you generalise the result in (ii) for any three numbers?
(I only need questions iii and iv)

Answer 1

Answer:

1- Least common multiple (LCM) of 120 and 126 is 2520

hope it helps

Answer 2

Answer:

GCF OF 120 AND 126 IS 6

Step-by-step explanation:

Step 1: Let's create a list of all the prime factors of 120 and 126:

Prime factors of 120:

As you can see below, the prime factors of 120 are 2, 2, 2, 3 and 5.

Let's illustrate the prime factorization of 120 in exponential form:

120 = 23x31x51

Prime factors of 126:

As you can see below, the prime factors of 126 are 2, 3, 3 and 7.

Let's illustrate the prime factorization of 126 in exponential form:

126 = 21x32x71

Step 2: Write down a list of all the common prime factors of 120 and 126:

As seen in the boxes above, the common prime factors of 120 and 126 are 2 and 3.

Step 3: All we have to do now is to multiply these common prime factors:

Find the product of all common prime factors by multiplying them:

21x31=6

Done!

According to our calculations above, the Greatest Common Factor of 120 and 126 is 6