Example: LCM of 4 and 8
Methods to find LCM: there are 3 methods to find LCM:
1. Multiplication method: follow the steps given below to find LCM by using this method:
Step 1: write multiples of the given numbers, until you did not find a common multiple.
Step 2: identify all the common multiples of the given numbers.
Step 3: mark the Least common multiple (LCM)
Example: find LCM of 4 and 8.
Step 1:
Multiples of 4: 4, 8, 12, 16, 20, 24……..
Multiples of 8: 8, 16, 24, 32…….
Step 2: Common multiples: 8, 16, 24….
Step 3: LCM = 8
Note: This method is helpful for smaller numbers, if you have numbers with a bigger difference, the calculation can be lengthy.
2. Division Method (GCF method): this method is applicable only when you have to find the LCM of two numbers. follow the steps given below to find LCM by using this method:
Step 1: find the GCF of the given numbers.
(to know how to find GCF? Click here)
Step 2: divide the product of the given numbers with GCF
Step 3: The quotient is the LCM of the given numbers.
Example: find the LCM of 6 and 72
Step 1: Prime factors of \(6=\ 2\times3\)
Prime factors of \(72=\ 2\times2\times2\times3\times3\)
GCF of 6 and 72 = 6
Step 2: now divide product of numbers with GCF, as;
\(\frac{6\times72}{6}=\ 72\)
Step 3: Lcm of 6 and 72 is 72
3. Exponential method: follow the steps given below to find LCM by using this method:
Step 1: find the prime factors of the given numbers and write into exponential form.
Step 2: find the product of all the factors of the given numbers with highest exponent
(do not repeat any factor).
Step 3: the product will be the LCM of given numbers.
Example: find the LCM of 8, 36 and 72
Step 1: \(Prime\ factors\ of\ 8=\ 2\times2\times2\)
\(=2^3\)
\(Prime\ factors\ of\ 36=\ 2\times2\times3\times3\)
\(=2^2\times3^2\)
\(Prime\ factors\ of\ 72=\ 2\times2\times2\times3\times3\)
\(=2^3\times3^2\)
Step 2: Product of the factors of all the numbers with highest exponent\(=2^3\times3^2=2\times2\times2\times3\times3\)
=72
Step 3: LCM of 8, 36 and 72 = 72
If the greatest number in the given set of numbers is divisible by the other numbers, then the greatest number will be the LCM of the given numbers.
Example: find the LCM of 8, 36 and 72
Now, 72 is divisible by both 8 and 36
Therefore, LCM of 8, 36 and 72= 72