LCM & HCF for Railway Group D – Short Tricks & Questions

 Mastering LCM & HCF for Railway Group D Exam – Short Tricks & Practice Questions

📜 Blog Description 

"Learn LCM & HCF tricks for the Railway Group D exam! 🚆 Master concepts, formulas, and shortcut techniques to solve problems quickly. Includes practice questions for better exam preparation!"

📌 Introduction

The topics of LCM (Least Common Multiple) and HCF (Highest Common Factor) are frequently tested in the Railway Group D Mathematics section. Questions from LCM & HCF appear in the Number System topic and play a crucial role in problem-solving, especially in time & work, time & distance, and ratio & proportion problems.

In this guide, we will discuss concepts, formulas, short tricks, and solved examples to help you ace these questions in Railway exams like RRB Group D, NTPC, ALP, and JE.

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🔢 What is LCM (Least Common Multiple)?

📌 Definition: The smallest number that is a multiple of two or more given numbers.

📌 Example: Find LCM of 4 and 6.
Multiples of 4: 4, 8, 12, 16, 20, …
Multiples of 6: 6, 12, 18, 24, …
👉 LCM = 12 (smallest common multiple)

📌 Formula:

$$\text{LCM} = \frac{\text{Product of numbers}}{\text{HCF of numbers}}$$

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🔢 What is HCF (Highest Common Factor)?

📌 Definition: The largest number that divides two or more given numbers completely.

📌 Example: Find HCF of 8 and 12.
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
👉 HCF = 4 (largest common factor)

📌 Formula:

$$\text{HCF} = \frac{\text{Product of numbers}}{\text{LCM of numbers}}$$

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💡 Shortcut Tricks to Find LCM & HCF

✔️ Prime Factorization Method

• Find prime factors of each number.
• LCM = Multiply highest power of each prime factor.
• HCF = Multiply lowest power of each prime factor.

📌 Example: Find LCM & HCF of 18 and 24.
Prime factors:
18 = 2 × 3²
24 = 2³ × 3
👉 LCM = 2³ × 3² = 72
👉 HCF = 2 × 3 = 6

✔️ Division Method

• Divide the greater number by the smaller number.
• Divide the remainder with the divisor until remainder = 0.
• Last divisor = HCF.

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🚆 Importance of LCM & HCF in Railway Group D Exam

✔️ Frequently asked in RRB Group D, NTPC, ALP & JE exams.
✔️ Used in Time & Work, Time & Distance, and Ratio & Proportion problems.
✔️ Helps in simplifying fractions and unitary method questions.

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🔥 Practice Questions for RRB Group D

🔹 Q1: Find LCM and HCF of 36 and 48.
🔹 Q2: The LCM of 18 and 24 is 72. Find their HCF.
🔹 Q3: Find the smallest number divisible by 6, 8, and 10.

📌 Comment your answers below!

📌 Categories:

• Railway Group D Study Material
• Mathematics Tricks
• Competitive Exam Notes