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
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Comment made by P.sujitha on Mar 6th 2019 at 5:11 am:
Find out LCM of 22,12
Comment made by Chandarvir Singh on Dec 1st 2019 at 7:19 am:
132
Comment made by shahab on Jul 11th 2019 at 3:37 am:
Help me hcf and lcm basic concept long tricks