Finding the LCM and HCF using

1
Finding the LCM and HCF using Prime Factor
Decomposition
We found that 22 x 5 20 and 25 32
The highest common factor is found by using the
prime factors that are common in both numbers
2 x 2 x 5 20 2 x 2 x 2 x 2 x 2 32
2
2
2
2
x
4
So the HCF of 20 and 32 is 4
The Lowest Common Multiple is found by using
HCF, then using all the numbers that are
different
5
2
2
2
2 x 2 x 5 20 2 x 2 x 2 x 2 x 2 32
2
2
2
2
HCF
x
x
x
160
x
x
So the LCM of 20 and 32 is 160
2
Prime Factor Decomposition

• Now answer these by using Prime Factor
  Decomposition
• Find the HCF and LCM of these pairs of numbers
• 24 and 36
• 27 and 36
• 32 and 48
• 56 and 152

2 x 2 x 2 x 3 24 2 x 2 x 3 x 3 36
HCF 2 x 2 x 3 12 LCM 12 x 2 x 3 72
3 x 3 x 3 27 2 x 2 x 3 x 3 36
HCF 3 x 3 9 LCM 9 x 2 x 2 x 3 108
2 x 2 x 2 x 2 x 2 32 2 x 2 x 2 x 2 x 3 48
HCF 2 x 2 x 2 x 2 16 LCM 16 x 2 x 3
96
2 x 2 x 2 x 7 56 2 x 2 x 39 152
HCF 2 x 2 4 LCM 4 x 7 x 39
1092