LCM & HCF Topic-wise Short Notes, Solutions, Methods, Tips, Tricks & Techniques to Solve Problems

LCM & HCF Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Useful For All Competitive Exams Like UPSC, SSC , BANK & RAILWAY

Posted By Careericons Team

Introduction to Factors and Multiples:

A factor of a number x is a whole number that divides into x evenly without a remainder. The factors of 50, for example, are 1, 2, 5, 10, 25, 50.

All the factors of a number can be reduced to prime numbers. Every number has a unique set of prime factors. The prime factors for 50 are 2 and 5. (2 × 5 × 5 = 50).

Complete LCM & HCF Based Aptitude MCQ Quiz For All Competitive Examinations

What is Least Common Multiple (L.C M.) & How to Find the LCM of the numbers?

The least common multiple (L.C.M.) is the smallest number that two or more numbers will divide into evenly.

LCM of numbers can be found by two types basically,

1. Using Prime factorization Or Factor Method
2. Using Division Method

Let's discuss these methods with example one by one;

Finding LCM by Prime Factorization Method:

Prime factorisation of numbers is one way to find the L.C.M. of given numbers.

Write the factors of two numbers. Strike out the factors in the second number, which are already there in the first number. Multiply the remaining factors of the second number with the factors of the first number to get the L.C.M. of the two numbers.

If there is a third number, write down its factors. Strike out the factors which are already included in the L.C.M. of the first two numbers. Multiply the remaining factors to get L.C.M. of the three numbers.

The process may be repeated for the other numbers if there are more.

Finding LCM by Division Method:

We can also find the L.C.M. by division method. Arrange the given numbers in a row. Divide by a number which divides exactly at least two of the given numbers. Write the quotients and undivided numbers in the next line.

Repeat the process until you get a line of numbers which are prime to one another. The product of the divisors and the undivided number is the required L.C.M..

Suppose we have to find the L.C.M. of

What is Highest Common Factor (H.C.F.) & How to Find the HCF of the numbers?

The greatest common factor (GCF), also called highest common factor (H.C.F.), is the largest common factor of two or more numbers. HCF is also called Greatest Common Divisor (GCD).

HCF of numbers can be found by two types basically,

1. Using Prime factorization Or Factor Method
2. Using Division Method

Let's discuss these methods with example one by one;

Finding HCF by Prime Factorisation method

Prime factorisation is a convenient way to find the H.C.F. of two or more numbers. After finding the prime factors of the numbers given, you have to find the common factors in pairs. Multiply these common factors to get the H.C.F.

"9" - Important Aptitude Rules, Formulas & Quick Tricks to Solve LCM & HCF Based Problems

In this list of rules, you will get an idea that How to solve all different types & kinds of LCM & HCF based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.

By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on LCM & HCF, Fractions in a faster approch.

Let's discuss the rules one by one with all LCM & HCF formulas with examples,

Rule 1:

Rule 2:

Rule 3:

Rule 4:

When a number is divided by a, b or c leaving same remainder 'r' in each case then that number must be k + r where k is LCM of a, b and c.

Rule 5:

When a number is divided by a, b or c leaving remainders p, q or r respectively such that

Rule 6:

The largest number which when divide the numbers a, b and c the remainders are same then that largest number is given by

H.C.F. of (a – b), (b – c) and (c – a).

Rule 7:

The largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by

H.C.F. of (a – p), (b – q) and (c – r).

Rule 8:

Greatest n digit number which when divided by three numbers p,q,r leaves no remainder will be

Rule 9:

The n digit largest number which when divided by p, q, r leaves remainder 'a' will be

Refer: Get all Topic-wsie Quantitatiive aptitude problems for upcoming competitive exams