Finding the HCF and LCM
To find the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of the numbers 12, 15, 18, and 27, we can follow these steps:
Step 1: Prime Factorization
First, we will perform the prime factorization for each number:
- 12: 2 x 2 x 3 = 22 x 31
- 15: 3 x 5 = 31 x 51
- 18: 2 x 3 x 3 = 21 x 32
- 27: 3 x 3 x 3 = 33
Step 2: Finding the HCF
The HCF is found by taking the lowest power of the common prime factors:
- Common prime factor: 3
Since the lowest power of 3 present in all factorizations is 31, we get:
HCF = 3
Step 3: Finding the LCM
The LCM is found by taking the highest power of all prime factors present in the numbers:
- For 2: highest power is 22 (from 12)
- For 3: highest power is 33 (from 27)
- For 5: highest power is 51 (from 15)
So, the LCM can be calculated as:
LCM = 22 x 33 x 51
Calculating this yields:
- 22 = 4
- 33 = 27
- 51 = 5
- Thus, LCM = 4 x 27 x 5 = 540
Final Results
The HCF and LCM of the numbers 12, 15, 18, and 27 are:
- HCF: 3
- LCM: 540