🔭 JSS 1🔢 Mathematics📅 First Term

Finding the LCM and HCF

Hello dear students! Today we will learn how to find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of numbers. These are useful when we share things equally or when we need to arrange things in groups. Let us see how easy it can be!

💡 What is HCF?

The HCF of two numbers is the biggest number that can divide both of them without leaving a remainder. Think of it as the biggest group size you can use to share items equally.

🧠 How to find HCF

Write the factors of each number. The common factors are the numbers that appear in both lists. The largest of those common factors is the HCF.

🔍 What is LCM?

The LCM of two numbers is the smallest number that both numbers can divide into exactly. It is the smallest size of a box that can hold items in both quantities without leaving any leftover.

📌 How to find LCM

Write the multiples of each number until you see a common multiple. The first common multiple you meet is the LCM.

✏️ Worked examples

Example 1: Find the HCF of 12 and 18.
Solution: Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors: 1, 2, 3, 6. The largest common factor is 6. So HCF(12,18)=6.
Example 2: Find the LCM of 4 and 5.
Solution: Multiples of 4: 4, 8, 12, 16, 20, ... Multiples of 5: 5, 10, 15, 20, ... The first common multiple is 20. So LCM(4,5)=20.
Example 3: Ada has 24 mangoes and Tunde has 36 mangoes. What is the biggest number of equal bunches they can each make?
Solution: Find HCF of 24 and 36. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. Common factors: 1,2,3,4,6,12. Largest is 12. So each can make bunches of 12 mangoes.
Example 4: Emeka wants to buy packets of biscuits that come in packs of 6 and 9. What is the smallest number of biscuits he can buy so that there are no leftovers?
Solution: Find LCM of 6 and 9. Multiples of 6: 6,12,18,24,30,36,... Multiples of 9: 9,18,27,36,... First common multiple is 18. So the smallest number is 18 biscuits.

⭐ Remember

  • HCF = Highest Common Factor, the biggest number that divides both numbers.
  • LCM = Least Common Multiple, the smallest number that both numbers divide into.
  • List factors to find HCF; list multiples to find LCM.
  • HCF helps when sharing equally; LCM helps when arranging together.
  • Check your work by dividing the HCF or LCM back into the original numbers.

🙌 Try this

Find the HCF and LCM of 8 and 14. Write the factors and multiples you used.

🔑 Log in to take the exam

10 questions · pass mark 50%

✨ Lesson written by AI from the Nigerian curriculum. Please tell us if you spot a mistake.