prime factor dec and hcf and lcm

Is there a better way to find the Highest Common Factor and Lowest Common Multiple of a Number?

1) Find the prime factor decomposition of 12 and 16.

20 = ……………………………………….

30 =………………………………………..

Find the Highest Common Factor and Lowest Common Multiple of 12 and 16.

HCF:……………………

LCM:…………………..

2) Find the prime factor decomposition of 20 and 30.

20 = ……………………………………….

30 = ………………………………………..

Find the Highest Common Factor and Lowest Common Multiple of 20 and 30.

HCF:……………………

LCM:…………………..

3) Find the prime factor decomposition of 45 and 60.

45 = ……………………………………….

60 = ………………………………………..

Find the Highest Common Factor and Lowest Common Multiple of 45 and 60.

HCF:……………………

LCM:…………………..

4) Find the prime factor decomposition of 54 and 72.

54 = ……………………………………….

72 = ………………………………………..

Find the Highest Common Factor and Lowest Common Multiple of 54 and 72.

HCF:……………………

LCM:…………………..

5) Looking over the previous 4 questions, can you find anyway to find the HCF and the LCM using the prime

factor decomposition of the numbers?

6) Use your methods from question five to find the HCF and LCM of 42 and 105.

7) Use your methods from question five to find the HCF and LCM of 240 and 900.