LCM of 162 and 168
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 162 and 168 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4536 as output. Here you can check the answer for Find the LCM of 162 and 168.
What is LCM of 162 and 168
Given Numbers are 162, 168
We can find the LCM of 162, 168 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 162 and 168
Multiples of 162 =162,324,486,648,810,972,1134,1296,1458,1620,1782,1944,2106,2268,2430,2592,2754,
Multiples of 168 =168,336,504,672,840,1008,1176,1344,1512,1680,1848,2016,2184,2352,2520,2688,2856,
Now, get the least common multiple of 162, 168 which is 4536
So, the LCM of 162, 168 is 4536.
Least Common Multiple (LCM) of 162 and 168 with the help of Prime Factorisation
One method for determining the LCM of 162 and 168 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 162's prime factorization:
| 2 | 162 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 162 are 2,3.
162 = 21×34
And this is 168's prime factorization:
| 2 | 168 |
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 168 are 2, 3,7.
168 = 23×31×71
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,7
.23×34×71 = 4536
This shows that the LCM of 162 and 168 is 4536.
How to Calculate the LCM of 162 and 168 Using Common Multiples
The first step in determining the Least Common Multiple of 162 and 168 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 162 and 168:
Lets look at the first ten multiples of these numbers, 162 and 168:
162,324,486,648,810,972,1134,1296,1458,2754 are the first ten multiples of 162.
168,336,504,672,840,1008,1176,1344,1512,2856 are the first ten multiples of 168.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 162 and 168, for example, are 1944, 2754, and 2688. 4536 is the least common multiple since it is the smallest.
162 and 168 have an LCM of 4536.
Least Common Multiple of 162 and 168 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 162 and 168, than apply into the LCM equation.
GCF(162,168) = 6
LCM(162,168) = ( 162 × 168) / 6
LCM(162,168) = 27216 / 6
LCM(162,168) = 4536
Related Least Common Multiples of 162
Related Least Common Multiples of 168
Frequently Asked Questions on LCM of 162 and 168
1. What is the LCM of 162 and 168?
The LCM of 162 and 168 is 4536.
2. How to find the lowest common multiple of 162 and 168?
To find the lowest common multiple of 162 and 168, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4536.
3. What are the Factors of 162?
Answer: Factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162. There are 10 integers that are factors of 162. The greatest factor of 162 is 162.
4. What are the Factors of 168?
Answer: Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168. There are 16 integers that are factors of 168. The greatest factor of 168 is 168.
5. How to Find the LCM of 162 and 168?Answer:
Least Common Multiple of 162 and 168 = 4536
Step 1: Find the prime factorization of 162
162 = 2 x 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 168
168 = 2 x 2 x 2 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4536 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 162 and 168 is 4536.