How do you find the HCF and LCM of 3 numbers? | Don't Memorise

TL;DR

Learn how to find the HCF and LCM of three numbers by reducing them to prime factors and multiplying shared factors for HCF and highest powers for LCM.

Transcript

We have to find the HCF and LCM of 18, 20 and 30. How do we find the HCF and LCM of three numbers together? The best way to do it is by reducing all numbers to its prime factors. And then write them in exponential form. Let's reduce 18 to its prime factors first. It is Divisible by 2, 2 times 9 is 18, and 3 times 3 is 9. So 18 can be written as a p... Read More

Key Insights

• ❓ Prime factorization simplifies the process of finding HCF and LCM.
• ✊ HCF is determined by the smallest powers of shared factors.
• ✋ LCM calculation involves the highest powers of each factor.
• 🧑‍🏭 Understanding the concept of shared factors is crucial in finding the HCF.
• 🤩 Highest power considerations are key to accurately determining the LCM.
• ✊ Exponential form representation aids in quick identification of prime factors and powers.
• 🖐️ HCF and LCM play essential roles in various mathematical applications.

Questions & Answers

Q: How do you find the prime factors of a number?

To find the prime factors of a number, divide it by the smallest prime number (starting from 2) until the quotient is a prime number. Repeat this process for the quotient until all factors are prime.

Q: Why is finding the HCF and LCM important in mathematics?

Finding the HCF and LCM helps in simplifying fractions, solving problems involving multiples or divisors, and is crucial in various mathematical operations like simplifying equations or calculating probabilities.

Q: What is the significance of using exponential form when dealing with HCF and LCM?

Expressing numbers in exponential form simplifies calculations by representing the prime factors and their powers clearly. It aids in identifying shared factors for HCF and highest powers for LCM accurately.

Q: Can the method for finding HCF and LCM of three numbers be applied to more numbers as well?

Yes, the method can be extended to any number of integers by reducing them to prime factors and applying the rules of HCF and LCM based on shared factors and highest powers.

Summary & Key Takeaways

• Reduce 18, 20, and 30 to prime factors, then write in exponential form.

• The HCF is found by multiplying the smallest powers of shared factors (2 in this case), while LCM is calculated by multiplying the highest powers (2^2 x 3^2 x 5).

• The process involves finding common factors, determining powers, and then identifying HCF and LCM using these values.