Methods to find HCF and LCM - Important formula and tricks

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Questions on HCF and LCM are easy but tricky. This article discusses HCF and LCM formulas, HCF and LCM tricks, important problems, etc.

hcf and lcm methods

 

HCF (Highest Common Factor)

Highest common factor or Greatest common measure(GCM) or Greatest common divisor(GCD) is the largest number that divides two or more given numbers.

 

Methods to find HCF 

1) Division method: This method uses successive division to find the HCF. To find the HCF of two numbers N1 and N2, the smaller of the two, say N1, divides N2. The remainder R1 then divides N1 followed by the remainder R2 dividing R1, and so on till a remainder of 0 is reachedThe last divisor is HCF.

2) Prime Factorization method: Express each one of the given numbers as a product of prime numbers. The product of the least powers of common prime factor gives HCF. For example,

The HCF of 96, 144 and 240 can be found by prime factorization of these numbers. 

96 = 25×31
144 = 24×32
240 = 24×31×51
HCF = 24×31 = 48

 

Tricks to Find HCF easily

Example: Find HCF of 12 and 16.

Find the difference between 12 and 16. The difference is 4. Now, check whether the numbers are divisible by the difference. 12 is divisible by 4 and 16 is divisible by 4.

Hence, the HCF is 4.

Example: Find HCF of 18 and 22.

Find the difference between 18 and 22. The difference is 4. Now, check whether the numbers are divisible by the difference. Both 18 and 22 are not divisible by 4. So take the factors of the difference. The factors of 4 are 2*2*1. Now, check whether the numbers are divisible by the factors. 18 and 22 are divisible by factor 2.

Hence, the HCF is 2.

Note: If there are more than two numbers, take the least difference.

 

LCM (Least Common Multiple)

The least number which is exactly divisible by each one of the given numbers is called their LCM.

 

Methods to find LCM 

Prime Factorisation method: After performing prime factorization of numbers, all prime numbers in their highest index are selected and multiplied to get the LCM. For example,

The LCM of 96, 144 and 240 can be found by prime factorization of these numbers.

96 25×31
144 24×32
240 24×31×51
LC25×32×51 = 1440

 

Tricks to Find LCM easily

Example: Find LCM of 2,4,8,16.

Choose the largest number. In this example, the largest number is 16. Check whether 16 is divisible by all other remaining numbers. 16 is divisible by 2, 4, 8. Hence, the LCM is 16.

Example: Find the LCM of 2,3,7,21.

Choose the largest number. The largest number is 21. Check whether 21 is divisible by all other remaining numbers. 21 is divisible by 3 and 7 but not by 2. So multiply 21 and 2. The result is 42. Now, check whether 42 is divisible by 2, 3, 7. Yes, 42 is divisible. Hence, the LCM is 42. 

 

HCF and LCM Formula and Tricks

  • Product of two numbers = Product of their HCF and LCM.
  • Two numbers are said to be co-primes if their HCF is 1.
  • HCF = HCF of Numerators/LCM of denominators.
  • LCM = LCM of Numerators/ HCF of Denominators.

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