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LCM and HCF

What is LCM and HCF ?

Hello students, welcome to my next article on Aptitude series. In this article we are going to learn about how to find LCM and HCF of any two numbers with simple trick. Lets firstly know about what is LCM and HCF.

LCM

The full form of LCM is Lowest Common Multiple or Lowest Common Divisor. LCM is the value which is divisible by the two given numbers. LCM is the method to find smallest common multiple between given two or more numbers.

How find LCM?

When we multiply any two numbers then we get value known as Multiple. For e.g, 4 is multiple of 2. LCM is calculated by simple formula. Let a & b two integers. Then formula is:
LCM (a,b) = (a x b)/GCD (a,b)
In case of fractional numbers the LCM is calculated by formula:
LCM (a / b) = LCM (a) / LCM (b).

LCM by Prime Factorisation Method

Prime factorial method is a very simple method to find LCM of any two or more numbers. Suppose there are three numbers 18, 12, 24. Lets write prime factors of all this numbers individually.
18 = 2 * 3 * 3
12 = 2 * 2 * 3
24 = 2 * 2 * 2 * 3
Now writing all prime factors of all three numbers together we get,
18 * 12 * 24 = 2 * 3 * 3 * 2 * 2 * 3 * 2 * 2 * 2 * 3.
By pairing the common prime factors we get there are three 2’s and two 3. So the LCM of 18, 12 and 24 will be,
LCM (18, 12, 24) = 2 * 2 * 2 * 3 * 3 = 72.

Properties of LCM
  • LCM is associative.
    LCM(a, b) = LCM(b, a).
  • LCM of any three numbers is commutative.
    LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM shows distributive property.
    LCM(da, db, dc) = dLCM(a, b, c).

HCF

The full form of HCF is Highest Common Factor. It also termed as GCD (Greatest Common Divisor). HCF is the value which divides each of two numbers. HCF is the simplest method to find greatest common divisor of any two or more numbers.

How find HCF?
  1. By Prime Factorisation Method

    2. Follow are some steps given to calculate HCF by prime factorisation method:

    • Write prime factors of each number.
    • Then list all the common factors of given numbers.
    • The HCF is the product of all common factors.
  2. By Division Method

    3. In above step you understood how to find HCF by prime factorization method. Now lets check how to find it using Division method. Follow this steps:

    • Write numbers horizontally by seperating with commas.
    • Find the smallest prime number which can exactly divide given numbers.
    • Now write quotient & repeat same process until no co-prime numbers is left.
    • Then the product of common prime factors we get on left hand side is HCF.

    Lets understand this method with help of example.

    Que: Find HCF of 30 and 75.
    Solution:
    image_src_byjus.com
    As per steps the HCF is the product of common prime factors mentioned on left side. Hence,
    HCF = 3 * 5 = 15.
Properties of HCF
  • HCF of any two or more numbers divide those numbers exactly.
  • HCF of all prime numbers always equals to 1.
  • HCF is always less than or equal to given numbers.

Practice Questions..

  1. Find LCM of 12, 14, 34.
  2. Find HCF of 75, 100
  3. MORE PROBLEMS ON LCM CLICK HERE.
  4. MORE PROBLEMS ON HCF CLICK HERE.

In closing...

So my dear students in this blog we learnt how to find LCM & HCF with simple tricks. If you not visited our previous blog on numbers then Click Here and explore it. Free to mail me if any query.
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