What is the difference between LCM and HCF and how to calculate these properly?

• The highest common factor of two or more two prime numbers is always 1.
• The LCM of two or more than two numbers will be their products.
• The HCF of the given numbers is never greater than the given numbers.
• The least common multiple of the given numbers is never smaller than any of the given numbers
• The product of two different numbers ‘a’ and ‘b’ is always equal to the

How to Calculate HCF and LCM properly?

⦁ Prime Factorization Method for LCM and HCF

• List the prime factors of the given numbers as:
  45 = 2 x 2 x 3 x 5
  60 = 3 x 3 x 5
• Multiply each factor that occurs for the maximum number of times

⦁ Division Method for LCM and HCF

• Divide the given number by the lowest prime number
• Write the number and quotient that are not divisible by the least prime number
• Further, divide these numbers with the other prime number
• Keep the division number until the reminder becomes the prime number or 1.
• Multiply the divisors and other prime numbers to get the LCM.

• Divide the larger number by the smaller one
• Further, divide the divisor of the above one by the reminder
• Keep dividing the divisor of step 2 with the reminder until the remainder becomes zero.

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For example, suppose two different numbers 12 and 18.
The greatest common factor of these numbers is:

The HCF of these two numbers by the division method is 6.

⦁ Using Online Calculators

Several useful online calculators are available to find the greatest common factor.
These converters allow you to check the HCF, LCM, or GCD of different numbers with just a single click.
These online calculators also allow you to select the desired method to find the LCM or HCF.
Most of the tools provide the following methods to check the highest common factor and least common multiple:

• Prime Factorization Method
• Division Method
• Euclidean Method
• Binary Stein’s Algorithm
• And more

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