# Real Numbers - Short Revision || CBSE Class 10 Mathematics || Infinity Learn Class 9&10 | Summary and Q&A

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February 18, 2023
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Infinity Learn NEET
Real Numbers - Short Revision || CBSE Class 10 Mathematics || Infinity Learn Class 9&10

## TL;DR

Solve multiple choice questions on real numbers, including finding the LCM and HCF of prime numbers.

## Key Insights

• 🟰 The LCM of two prime numbers is equal to their product.
• 😆 When given the prime factorization of a number, the larger prime factor corresponds to p and the smaller one corresponds to q when p is greater than q.
• ✋ To find the LCM, take all prime numbers involved and their highest powers.
• ✊ To find the HCF, take the common factors (prime numbers) and their least powers.
• 🟰 The product of two numbers is equal to the product of their LCM and HCF.
• 🧑‍🏭 The HCF of two numbers is always a factor of their LCM.
• #️⃣ The LCM of two numbers is always a multiple of their HCF.

## Transcript

hello everybody Welcome to the infinity learned by SRI chaitanya I am Miss bio maths educator and we are over here to do five McQ questions on the chapter real numbers so let's start with it so the very first question over here is the LCM of two prime numbers p and Q where p is greater than Q is 323 you have to find the value of 3p minus Q over her... Read More

### Q: How do you find the LCM of two prime numbers?

The LCM of two prime numbers is equal to the product of the numbers itself. In the given example, the LCM of p and q is equal to p*q.

### Q: How do you determine which value is p and which is q in the prime factorization of a given number?

If it is given that p is greater than q, then the larger prime factor corresponds to p and the smaller one corresponds to q.

### Q: How do you find the LCM when numbers are written in terms of prime factors?

To find the LCM, take every prime number involved in all of the numbers and then take the highest power of each prime factor.

### Q: How do you find the HCF of two numbers given their prime factorizations?

To find the HCF, take the common factors (prime numbers) and then take the least power of each common factor.

## Summary & Key Takeaways

• The LCM of two prime numbers, p and q, can be found by multiplying them together. In the given example, pq = 1719, resulting in 323.

• When given the prime factorization of a number, determine which value is p and which is q based on the condition that p is greater than q.

• To find the LCM of two numbers written in terms of prime factors, take the highest powers of each prime factor involved. For example, LCM(X^5Y^7, X^6Y^3) is X^6*Y^7.