The Ultimate Guide to LCM and HCF: Tricks, Shortcuts, and Solved Examples

Are you looking for the fastest way to find the LCM and HCF? Whether you are a Grade 5 student doing homework, a parent trying to explain math to kids, or a puzzle lover solving a viral riddle, you are in the right place.

This guide answers every common question about HCF (Highest Common Factor) and LCM (Least Common Multiple), from the "2-second short trick" to the solution for complex number sequences.

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⚡ Part 1: The Short Tricks (How to Calculate in 2 Seconds)

Many people ask, "What is the easiest way to find the LCM?" or "Is there a short trick for HCF?" Here are the mental math hacks used by experts.

1. The "Big Number" Trick for LCM

Query: How to find LCM in 2 seconds?
Instead of listing multiples, look at the largest number in your set.

1. Pick the largest number.
2. Check: Do the smaller numbers divide into it evenly?
3. If YES: The largest number is your LCM.
4. If NO: Multiply the largest number by 2, 3, or 4 until the others fit.

2. The "Difference" Trick for HCF

Query: What is the shortest way to find the HCF?
Use the Subtraction Method.

1. Find the difference between the two numbers.
2. The HCF is either that difference OR a factor of that difference.

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📚 Part 2: Solved Problems (Answers to Your Specific Questions)

We have calculated the answers to the specific long-tail math questions often searched online.

Q: What is the HCF of 24 and 36?

Answer: 12.
(Using the difference method: 36 - 24 = 12).

Q: How to find the LCM of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?

Answer: 2,520.

• Why? You need the smallest number divisible by all digits 1-10.
• Take the highest powers of primes: 2³ (8), 3² (9), 5, 7.
• Calculation: 8 × 9 × 5 × 7 = 2520.

Q: What is the HCF of 9, 10, 12, 25, 18, 35, 21, 40?

Answer: 1.

• The Shortcut: You don't need to calculate the whole list! Look at the first two numbers: 9 and 10.
• They are "consecutive integers" (neighbors). Consecutive integers never share any common factor except 1.
• Therefore, the HCF of the entire group must be 1.

Q: "Can you find the mistake 1 2 3 4 5 6 7 8 9?"

Answer: This is usually a viral visual puzzle, not a math problem.

• The Math: There is no mistake in the numbers; they are in the correct order.
• The Trick: In most versions of this image, the mistake is in the text question itself (e.g., the word "the" is written twice, like "Can you find the the mistake?") or the word "Mistake" is misspelled.

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🏫 Part 3: The Basics (For Kids & Grade 5)

How do you explain HCF and LCM to kids?

Avoid complex jargon. Use these real-world analogies:

What are the three methods to find LCM?

If you are answering a "Grade 5" exam question, these are the expected methods:

1. Listing Multiples: Writing out the multiplication table (3, 6, 9, 12...) until a number matches.
2. Prime Factorization: Breaking numbers into trees (12 = 2 × 2 × 3).
3. Division Method: The "Ladder" method where you divide all numbers by primes until you reach 1.

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📝 Summary Cheat Sheet

For a quick reference, here are the direct answers to the most popular queries: