HCF & LCM

Let’s dive into HCF and LCM, two ideas that help us understand how numbers connect through their factors. Think of them like finding the best way to share things out (HCF) and the best way to combine things together (LCM)

 

What is HCF?

The HCF or Highest Common Factor of two numbers is the largest number that can divide both of them without leaving a remainder. Imagine having two groups of objects, like sets of marbles or pencils. The HCF tells you the biggest set size where you can divide both groups evenly without leftovers.

How to Find the HCF

1. Factorize each number into its prime factors.
2. Identify the common factors between the two sets.
3. Multiply the common prime factors together. The result is your HCF!

 

Find the HCF and LCM of 18 and 24

1. Prime Factorization:

   • 18: $$18 = 2 \times 3 \times 3 = 2 \times 3^2$$
   • 24: $$24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3$$
2. HCF:
   • Common Factors: $2$ and $3$
   • Multiply the lowest powers of each common prime factor: $$HCF = 2^1 \times 3^1 = 6$$

So the HCF of 18 and 24 is 6

 

 

 

 

 

 

What is LCM?

The LCM or Lowest Common Multiple is the smallest number that both original numbers can divide into. Imagine setting up two flashing lights with different timings. The LCM tells you when they’ll flash together again.

How to Find the LCM

1. Factorize each number into its prime factors.
2. Use all the prime factors, taking the highest power of each one.
3. Multiply these together to get the LCM

 

Find the  LCM of 18 and 24

1. Prime Factorization:

   • 18: $$18 = 2 \times 3 \times 3 = 2 \times 3^2$$
   • 24: $$24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3$$
2. LCM:
   • Take the highest powers of each prime factor: $$HCF = 2^3 \times 3^2 = 72$$

So the LCM of 18 and 24 is 72