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)

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 =
The highest power of 7 here = 7
Hence LCM = 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
24 = χ 3
9 =
36 = χ
90 = 2 χ 5 χ

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 =
The highest power of 3 here =
The highest power of 5 here = 5
Hence LCM = χ 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

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





Hence Least common multiple (L.C.M) of 8 and 14 = 2 × 4 × 7 = 56

One Response 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

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