LCM & HCF are fundamental concepts in number theory. In this blog, we will delve into the definitions, properties, and methods of finding LCM and HCF.
LCM:
LCM stands for Lowest Common Multiple the smallest common multiple of two or more integers. It represents the smallest number that is divisible by each of the given numbers without leaving a remainder.
LCM Calculation:
Prime Factorization:
- Determine prime factors for each of the numbers whose LCM is to be found.
- After finding the prime factors write them in their exponent form
- Find the product of only those prime factors that have the highest power .
- The product of these factors with the highest powers is the LCM of the given numbers.
Prime Factors of 75= 3*5*5Prime Factors of 100=2*2*5*5
LCM(75,100)= 3*2*2*5*5=300
Division Method:
- To find the LCM of numbers by the division method, we divide the numbers with prime numbers and stop the division process when we get only 1 in the final row.
Let's find LCM of 75 & 100 using division method.
Now when you multiply the list of dividing number you will get 300.
HCF:
HCF stands for Highest Common Factor and it is also known as Greatest Common Divisor (GCD), is the largest positive integer that divides two or more given numbers without leaving a remainder.
HCF Calculation:
Prime Factorization:
- Determine the prime factors of those numbers.
- Calculate product of the prime factors that are common to each of the given numbers.
Let's find HCF of 75 & 100 using prime factorization.
Prime Factors of 75= 3*5*5
Prime Factors of 100=2*2*5*5
HCF(75,100)= 5*5=25
Division Method:
- Identify the largest and the smallest number.
- Divide largest number from smallest number. Check for the remainder.
- Now make the remaider as the divisor and the divisor from step 2 as dividend.
- Perform the division.
- Repeat the above steps till the remainder is zero.
- Last divisor is the HCF.
Let's find HCF of 75 & 100 using division method.
From step 2, we have divisor as 25 and remainder as zero. Hence 25 is HCF of 75 & 100.
Division method could be time consuming for more than 2 numbers.
Procedure for finding HCF of 3 numbers:
- Determine the HCF of the any 2 numbers.
- Then find HCF of 3 number and HCF(2 numbers) that was found in the previous step.
Procedure for finding HCF of 4 numbers:
- Group the numbers into 2 groups.
- Determine HCF of group 1 and group 2 separately.
- Find HCF of HCFs we got in previous step. This will be HCF of all four numbers.
LCM × HCF = Product of Numbers. (This is applicable only if we have 2 numbers)
Click Here to test your knowledge on LCM & HCF.
Instructions:
- Choose LCM & HCF from 'Select test Topic' drop down.
- Each correct selection results in 1 mark.
- Each in-correct selection results in -0.33 mark.
- All the Best