LCM and HCF Shortcut Tricks and Formulas

LCM and HCF Shortcut Tricks - Page 2
LCM and HCF Important Questions - Page 3
LCM and HCF Video Lecture - Page 4

Least Common Multiple (LCM) & Highest Common Factor(H.C.F)

Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers.
Example: LCM of 3 and 4 = 12 because 12 is the smallest multiple which is common to 3 and 4 (In other words, 12 is the smallest number which is divisible by both 3 and 4)

LCM Example and Shortcuts

How to find out LCM using prime factorization method

We can find LCM using prime factorization method in the following steps

Step1 : Express each number as a product of prime factors.
Step2 : LCM = The product of highest powers of all prime factors

Example 1 : Find out LCM of 8 and 14
Step1 :
Express each number as a product of prime factors. (Reference: Prime Factorization and how to find out Prime Factorization)
8 = 2^{3}
14 = 2 χ 7

Step2 : LCM = The product of highest powers of all prime factors
Here the prime factors are 2 and 7
The highest power of 2 here = 2^{3}
The highest power of 7 here = 7
Hence LCM = 2^{3} χ 7

Example 2 : Find out LCM of 18, 24, 9, 36 and 90

Step1 : Express each number as a product of prime factors (Reference: Prime Factorization and how to find out Prime Factorization).

18 = 2 χ 3^{2}
24 = 2^{3} χ 3
9 = 3^{2}
36 = 2^{3} χ 3^{2}
90 = 2 χ 5 χ 3^{2}

Step2 : LCM = The product of highest powers of all prime factors
Here the prime factors are 2, 3 and 5
The highest power of 2 here = 2^{3}
The highest power of 3 here = 3^{2}
The highest power of 5 here = 5
Hence LCM = 2^{3} χ 3^{2} χ 5 = 360
Hence Least common multiple (L.C.M) of 18, 24, 9, 36 and 90 = 2 × 2 × 3 × 3 × 2 × 5 = 360

How to find out LCM using Division Method (shortcut)

Step 1 : Write the given numbers in a horizontal line separated by commas.
Step 2 : Divide the given numbers by the smallest prime number which can exactly divide at least two of the given numbers.
Step 3 : Write the quotients and undivided numbers in a line below the first.
Step 4 : Repeat the process until we reach a stage where no prime factor is common to any two numbers in the row.
Step 5 : LCM = The product of all the divisors and the numbers in the last line.

Example 1 : Find out LCM of 8 and 14
2\:\begin{array}{|c}8,14\\\hline \end{array}
 \:\begin{array}{c}&4,7\end{array}

Example 2 : Find out LCM of 18, 24, 9, 36 and 90
2\:\begin{array}{|c}18, 24, 9, 36, 90 \\\hline \end{array}
2\:\begin{array}{|c}9, 12, 9, 18, 45 \\\hline \end{array}
 3\:\begin{array}{|c}9, 6, 9, 9, 45 \\\hline \end{array}
 3\:\begin{array}{|c}3, 2, 3, 3, 15 \\\hline \end{array}
 \:\begin{array}{c}&1,2,1,1,5\end{array}
Hence Least common multiple (L.C.M) of 8 and 14 = 2 × 4 × 7 = 56

Latest Jobs

  1. Type
    Job Notification
    Job
    IBPS Recruitment Specialist Officers 1163 Vacancies - Last Date 26-11-2019
    Location
    Anywhere
    Date Posted
    20 Nov 2019
  2. Type
    Job Notification
    Job
    CISF Recruitment for 300 HEAD CONSTABLE - SPORTS QUOTA - Last Date 17-12-2019
    Location
    Anywhere
    Date Posted
    19 Nov 2019
  3. Type
    Job Notification
    Job
    IOCL Invites Application for 1542 Apprentice - Last Date 15-11-2019
    Location
    Anywhere
    Date Posted
    5 Nov 2019
  4. Type
    Job Notification
    Job
    SAIL Bhilai Recruitment of Operator cum Technician, Nurse, Fire Station Officer, and more - Last Date 15-11-2019
    Location
    Vaishali NagarChhattisgarh, India
    Date Posted
    5 Nov 2019
  5. Type
    Job Notification
    Job
    Naval Ship Repair Yard, Karnataka Recruitment of 145 ITI qualified. - Last Date 01-12-2019
    Location
    KarwarKarnataka, India
    Date Posted
    5 Nov 2019
  6. Type
    Job Notification
    Job
    IIT Dhanbad 191 Recruitment Engineers, Staff Nurse and others - Last Date 14-12-2019
    Location
    DhanbadJharkhand, India
    Date Posted
    5 Nov 2019
  7. Type
    Job Notification
    Job
    INDIAN Bank Recruitment of 115 Security Guard cum Peon – Last Date 08-11-2019
    Location
    Anywhere
    Date Posted
    28 Oct 2019
  8. Type
    Job Notification
    Job
    AIIMS Rishikesh 184 Recruitment Staff Nurse, Assistant Nursing Superintendent – Last Date 30-11-2019
    Location
    RishikeshUttarakhand, India
    Date Posted
    28 Oct 2019
  9. Type
    Job Notification
    Job
    Cement Corporation of India Recruitment of 60 Artisan Trainees - Last Date - 25-10-2019
    Location
    Anywhere
    Date Posted
    25 Oct 2019
  10. Type
    Job Notification
    Job
    MFL Recruitment of 93 Engineering, Management Trainees, Assistant Trainees - Last Date 25-10-2019
    Location
    ChennaiTamil Nadu, India
    Date Posted
    25 Oct 2019

Jobs by Category

Syllabus and Previous Papers

3 Responses to “LCM and HCF Shortcut Tricks and Formulas”

  1. Comment made by P.sujitha on Mar 6th 2019 at 5:11 am: Reply

    Find out LCM of 22,12

    • Comment made by Chandarvir Singh on Dec 1st 2019 at 7:19 am: Reply

      132

  2. Comment made by shahab on Jul 11th 2019 at 3:37 am: Reply

    Help me hcf and lcm basic concept long tricks

Leave a Reply

Your email address will not be published. Required fields are marked *