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(6) Highest Common Factor and Lowest Common Multiple

Highest Common Factor

a)(i) List all the factors of 90. There are 12 in total.
   (ii) List all the factors of 105. There are 8 in total.
*List the numbers in ascending order separated by commas.

b) What is the Highest Common Factor of 90 and 105?

a)(i)

a)(ii)

b)

Lowest Common Multiple

a)(i) List the first eight multiples of 90.
   (ii) List the first eight multiples of 105.
*List the numbers in ascending order separated by commas.

b) What is the Lowest Common Multiple of 90 and 105?

a)(i)

a)(ii)

b)

Investigate

Take a close look at the previous examples and see if you can find a method without writing all the multiples and factors.

a) What is the HCF of 735 and 756?
b) What is the LCM of 735 and 756?

a)

b)

a) What is the HCF of 8580 and 9240?
b) What is the LCM of 8580 and 9240?

a)

b)

Practice

Find the highest common factor for the following pairs of numbers.
*Write your answers as a product of prime factors in ascending order (ie. $2^3 \times 3^2 \times 5$)
Copy this $\times$ or type \times for the multiply symbol

a) 630 and 900

b) 630 and 792

c) 792 and 900

d) 792 and 1815

e) 630 and 9240

Find the lowest common multiple for the following pairs of numbers.
*Write your answers as a product of prime factors in ascending order (ie. $2^3 \times 3^2 \times 5$)
Copy this $\times$ or type \times for the multiply symbol

a) 630 and 900

b) 630 and 792

c) 792 and 900

d) 792 and 1815

e) 630 and 9240