HCF & LCM Shortcuts
Find factors and multiples instantly.
Core Concepts
Traditional HCF methods can be long. Vedic Maths uses difference checking + remainder logic for fast results.
Method 1: Difference Method
Best when numbers are close.
1. Find the difference of the two numbers.
2. If both numbers divide by this difference → that is HCF.
3. If not, check factors of the difference.
Example: HCF of 12 and 16. Diff = 4. Both divisible by 4. HCF = 4.
Method 2: Remainder Method
Universal Method (Vedic-style Euclid).
1. Divide bigger by smaller.
2. Use remainder as new divisor.
3. Repeat until remainder is 0. Last divisor is HCF.
Example: 30 ÷ 18 (Rem 12) → 18 ÷ 12 (Rem 6) → 12 ÷ 6 (Rem 0). HCF = 6.
Finding LCM (Always Works)
Once HCF is known, use the formula:
LCM = (First × Second) ÷ HCF
Vedic Speed Tip: Always divide first, then multiply.
Example: LCM of 12 and 15 (HCF=3). 12÷3 = 4. Then 4×15 = 60.
Solved Examples
Example 1: HCF of 12 and 16
Question: Find HCF of 12 and 16.
• Difference: 16 - 12 = 4.
• Check: Is 12 divisible by 4? Yes. Is 16 divisible by 4? Yes.
• Answer: HCF is 4.
Example 2: HCF of 21 and 35
Question: Find HCF of 21 and 35.
• Difference: 35 - 21 = 14.
• Check: Is 21 divisible by 14? No.
• Factors of 14: 7, 2.
• Check 7: 21÷7=3 (Yes), 35÷7=5 (Yes).
• Answer: HCF is 7.
Example 3: LCM of 4 and 6
Question: Find LCM of 4 and 6.
• Step 1 (Find HCF): Diff is 2. HCF is 2.
• Step 2 (Formula): (4 × 6) ÷ 2.
• Calculate: 24 ÷ 2 = 12.
• Answer: LCM is 12.
Example 4: LCM of 12 and 15
Question: Find LCM of 12 and 15.
• Step 1 (Find HCF): Diff is 3. HCF is 3.
• Step 2 (Formula): (12 × 15) ÷ 3.
• Tip: Divide first! 12 ÷ 3 = 4. Then 4 × 15 = 60.
• Answer: LCM is 60.
