Least common multiple and Least common denominator

Least common multiple or LCM of two numbers is the smallest number that is multiple of both.
How to find the least common multiple?
Methods to find the LCM:
1. Prime factorization method – Following steps are followed to find LCM by prime factorization method:
• Find the factors of numbers whose LCM has to be obtained.
• Find the common factors of all the numbers.
• Find the factors that are not common.
• LCM is the product of common factors and the factors that are not common
LCM = (Product of common factors) X (Product of uncommon factors)
2. Common division method – Following steps are followed to find LCM by common division method: -
• Arrange numbers together separated by commas.
• Start with smallest prime number and keep on dividing till none of the numbers can further be divided.
• Multiply all the factors together to find the LCM.
The common division method is useful for finding the LCM of more than two numbers.
Least common denominator
Least common denominator is calculated for adding and subtracting the fractions. We cannot add or subtract any fraction before finding the least common denominator.
 How to find the least common denominator? (Finding the least common denominator)
Least common denominator finder
Suppose if we have two fractions such as 7/4 and 5/6.
To add these fractions, we need to find the least common denominator and o find the least common denominator of these two fractions, we find the least common multiple of their denominators i.e. LCM of 4 and 6.
4 = 2 X 2
6 = 2 X 3
2 is the only common factor and 2, 3 are the factors that are not common.
Product of common factors = 2
Product of factors that are not common = 2 X 3 = 6
LCM = (Product of common factors) X (Product of factors that are not common)
= (2) X (2 X 3) = 2 X 6 = 12
Hence the LCM of 4 and 6 is 12.
The least common denominator of 7/4 and 5/6 is 12
7/4 + 5/6 = 7*3/4*3 + 5*2/6*2 = 21/12 + 10/12 = 31/12