LCM & GCD Calculator

Introduction to the LCM & GCD Calculator

The LCM & GCD Calculator is a free online tool that finds the Lowest Common Multiple and Greatest Common Divisor (also called HCF) of two or more numbers. The core relation is LCM(a, b) x GCD(a, b) = a x b, so finding one gives the other instantly.

Indian students from class 5 to college, competitive exam aspirants and engineering candidates use this LCM HCF tool every week. Whether you study CBSE class 6 in Mumbai, CTET preparation in Lucknow or quantitative aptitude in Bengaluru for IBPS PO, the prime factorisation and Euclidean algorithm stay fundamental. Related concepts like prime numbers, factors, divisibility rules and fractions all sit on top of LCM and HCF.

Inputs are 2 to 10 positive integers. Outputs are the LCM, GCD, prime factorisation breakdown and step-by-step working that students can copy in homework or exam notebooks.

Who Should Use This LCM & GCD Calculator

1. CBSE class 6-8 students in Delhi solving NCERT exercises on multiples and factors.
2. 2. Engineering aspirants in Kota practising number theory for JEE Main quantitative section.
3. 3. CAT and SSC CGL aspirants in Pune drilling LCM-HCF based ratio and proportion problems.
4. 4. Bank exam aspirants in Hyderabad solving time, speed, distance and work questions in IBPS PO.
5. 5. Tuition teachers in Chennai preparing class worksheets and practice tests for math students.

Tips for LCM and HCF Problems

Smart LCM and HCF Tips

1. For two numbers, find HCF first using Euclidean division, then LCM = (a x b) / HCF. Saves 2-3 minutes per question.
2. 2. Practise prime factorisation up to 100, since competitive exam answers usually involve products of 2, 3, 5, 7, 11, 13.
3. 3. Use the listing method only for small numbers below 30, otherwise factorisation is faster.
4. 4. Buy a basic scientific calculator like Casio FX-82MS (around Rs 800) for school but solve manually in exams since electronic calculators are banned in CBSE and JEE.
5. 5. Memorise this rule: LCM of two co-prime numbers (HCF = 1) is simply their product.

Formula Explanation

Core LCM & GCD Formula

GCD (Euclidean): GCD(a, b) = GCD(b, a mod b), recursive until b = 0 LCM = (a x b) / GCD(a, b) For 3+ numbers: GCD(a, b, c) = GCD(GCD(a, b), c) LCM(a, b, c) = LCM(LCM(a, b), c)

Where:

• mod = remainder after division
• • GCD = greatest common divisor (also called HCF)
• • LCM = lowest common multiple

Example: Numbers 12 and 18. GCD: 18 mod 12 = 6, 12 mod 6 = 0, so GCD = 6. LCM = (12 x 18) / 6 = 36.

LCM & GCD Quick Reference Table

Numbers	Prime Factors	GCD (HCF)	LCM
12, 18	2x2x3, 2x3x3	6	36
24, 36	2^3 x 3, 2^2 x 3^2	12	72
15, 25	3 x 5, 5 x 5	5	75
30, 45, 60	mixed	15	180
8, 9	2^3, 3^2	1 (co-prime)	72

Real-World Example

Example: Aditi's Class 6 Math Problem

Meet Aditi, an 11 year old CBSE class 6 student from Pune who needs to find the LCM and HCF of 36 and 48 for tomorrow's math test on multiples and factors.

Step 1: Prime factorise: 36 = 2 x 2 x 3 x 3 and 48 = 2 x 2 x 2 x 2 x 3. Step 2: HCF = product of common prime factors = 2 x 2 x 3 = 12. Step 3: LCM = (36 x 48) / 12 = 1728 / 12 = 144.

Result: Aditi confirms LCM = 144 and HCF = 12. She also verifies using the relation 36 x 48 = 1728 = 144 x 12, and scores full 5 marks on the test.

Frequently Asked Questions About LCM & GCD

Indian school students, competitive exam aspirants and tuition teachers often ask about quick LCM and HCF tricks, the relationship between them and how to handle 3 or more numbers. The answers below cover NCERT patterns, common exam shortcuts and the Euclidean algorithm in simple steps.