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Full Form of LCM and HCL

authorImageRanvijay Singh4 Sept, 2023
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LCM and HCL
The full form of LCM in math is the least common factor and the full form of HCF is the highest common factor. LCM of two or more numbers gives the least number that is divisible by those numbers, whereas the HCF of two or more numbers gives the greatest factor present between those numbers. LCM is also known as the least common divisor (LCD)and HCF is also known as the greatest common factor(GCF). There are two methods to calculate LCM and HCF namely prime factorization method and the division method. Among the given methods of evaluation, the division method is considered to be easier. 

Definition of LCM and HCF

The least common multiple or LCM of two numbers say A and B, is denoted by LCM (A, B). The LCM is the least positive integer that is divisible by both a and b. For example, take two positive integers 5 and 10. Multiples of 5: 5,10,15,20,25,30… Multiples of 10: 10,20,30,40…. The common multiples for 5 and 10 are 10,20,30,40… The least common multiple is 10. To find out the LCM of 18 and 15. 
3 18, 15
3 6, 5
2 2, 5
5 1, 5
1, 1
LCM of 18 and 15 = 3 × 3 × 2 × 5 = 90 The greatest common divisor(GCD) or the HCF of two or more positive integers is the largest positive integer that divides the numbers without leaving a remainder. For example, take 10 and 16. The H.C.F. of 10 and 16 will be 2 because the highest number that can divide both 10 and 16 is 2.

How to Calculate LCM and HCF

The formula which includes both HCF and LCM is:
Product of two numbers = (HCF of the two numbers) x (LCM of the two numbers)
The above relation between HCF and LCM is only valid for the product of two numbers.

Methods to Calculate LCM and HCF

There are two methods to find the HCF and LCM of given numbers.
  1. Prime factorization method
  2. Division method
HCF by Prime Factorization Method The highest common factor of 100, 64, and 120. The prime factors of 100, 64, and 120 are listed below. 100 = 2 × 2 × 5 × 5  64 = 2 × 2 × 2 × 2 × 2 × 2  120 = 2 × 2 × 2 × 3 × 5  The common factors of 100, 64 and 120 are 2 × 2  = 4 Therefore, HCF (100, 64, 120) = 4 HCF by Division Method To find the HCF of more than 3 numbers follow the given steps:
  1. Divide larger number by smaller number
  2. Divide the divisor of the above step by the remainder
  3. Divide the divisor of step 2 by the remainder keep repeating until you get 0 as the remainder.
  4. The divisor of the last step would be the HCF.
Example: Find the HCF of 100 and 120 by division method. Since 120>100, the dividend will be 120 and the divisor will be 100. Using the division method, we get: 100) 120 ( 1                      100                          20) 100 ( 5                                      100                                        XX Hence, 20 is the highest number which divides 100 and 120. Therefore, HCF (100, 120) = 20 LCM by Prime Factorization Method To calculate the LCM of two numbers 40 and 55:
  • List the prime factors of each number. 40 = 2 × 2 × 2 × 5 55 = 5 × 11
  • Multiply each factor by the number of times it occurs in any number.
Multiply the factor by the most number of times it occurs, If the same multiple occurs more than once in both the given numbers. 2: three times 5: one times 11: one time LCM = 2 × 2 ×  2 × 5 × 11 = 440 LCM by Division Method Find LCM of (40,55) by division method.
5 40,55
2 8,11
2 4,11
2 2,11
11 1,11
1,1
Therefore, LCM of 40 and 55 = 5 × 2 × 2 × 2 × 11 = 440

Examples of LCM and HCF

Example 1. What is the least common multiplier of 52 and 13? Solution: Given two numbers 52 and 13. The LCM by division method.
13 52,13
2 4,1
2 2,1
1,1
  Therefore, LCM(52,13) = 13 × 2 × 2  = 52 Example 2. Find the product of two numbers whose HCF is 20 and LCM is 6. Solution: Product of two numbers = HCF x LCM. The product is not possible as the given HCF is greater than the given LCM which is not possible. Example 3. Find the Highest Common Factor of 20, 30 and 40. Solution: Given, three numbers as 20, 30 and 40. We know that, 20 = 2 × 2 × 5 30 = 2 × 3 × 5 40 = 2 × 2 × 2 × 5 2 and 5 are the only common factor for all three numbers. Therefore, 10 is the HCF of 20, 30 and 40. [wp-faq-schema title=" Full Form of LCM and HCL FAQs" accordion=1]

What is the full form of HCF in Maths? Explain HCF with an example.

HCF stands for the Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. For example, 3 is the HCF of 9 and 15.

What is the full form of LCM in Maths? Explain LCM with an example.

LCM stands for the Least common multiple. LCM is the smallest number that is divisible by two or more given numbers. For example, LCM of 4 and 10 is 2.

What is the formula for HCF and LCM?

Product of two numbers = (HCF of the two numbers) x (LCM of the two numbers). Hence,  HCF of two numbers = (Product of two numbers)/(L.C.M of two numbers) LCM of two numbers = (Product of two numbers)/(H.C.F. of two numbers)

How can we find the LCM and HCF?

We can find LCM and HCF using the prime factorization method and long division method.
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