It is easy to find the LCM of 138 and 145 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 20010 as output. Here you can check the answer for Find the LCM of 138 and 145.
Given Numbers are 138, 145
We can find the LCM of 138, 145 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 138 and 145
Multiples of 138 =138,276,414,552,690,828,966,1104,1242,1380,1518,1656,1794,1932,2070,2208,2346,
Multiples of 145 =145,290,435,580,725,870,1015,1160,1305,1450,1595,1740,1885,2030,2175,2320,2465,
Now, get the least common multiple of 138, 145 which is 20010
So, the LCM of 138, 145 is 20010.
One method for determining the LCM of 138 and 145 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 138's prime factorization:2 | 138 |
3 | 69 |
23 | 23 |
1 |
Prime factors of 138 are 2, 3,23.
138 = 21×31×231
And this is 145's prime factorization:
5 | 145 |
29 | 29 |
1 |
Prime factors of 145 are 5,29.
145 = 51×291
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, 3,23, 5,29
.21×31×51×231×291 = 20010
This shows that the LCM of 138 and 145 is 20010.
The first step in determining the Least Common Multiple of 138 and 145 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 138 and 145:
Lets look at the first ten multiples of these numbers, 138 and 145:
138,276,414,552,690,828,966,1104,1242,2346 are the first ten multiples of 138.
145,290,435,580,725,870,1015,1160,1305,2465 are the first ten multiples of 145.
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 138 and 145, for example, are 1656, 2346, and 2320. 20010 is the least common multiple since it is the smallest.
138 and 145 have an LCM of 20010.
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 138 and 145, than apply into the LCM equation.
GCF(138,145) = 1
LCM(138,145) = ( 138 × 145) / 1
LCM(138,145) = 20010 / 1
LCM(138,145) = 20010
1. What is the LCM of 138 and 145?
The LCM of 138 and 145 is 20010.
2. How to find the lowest common multiple of 138 and 145?
To find the lowest common multiple of 138 and 145, we have to get the multip;es of both numbers and identify the least common multiple in them which is 20010.
3. What are the Factors of 138?
Answer: Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138. There are 8 integers that are factors of 138. The greatest factor of 138 is 138.
4. What are the Factors of 145?
Answer: Factors of 145 are 1, 5, 29, 145. There are 4 integers that are factors of 145. The greatest factor of 145 is 145.
5. How to Find the LCM of 138 and 145?Answer:
Least Common Multiple of 138 and 145 = 20010
Step 1: Find the prime factorization of 138
138 = 2 x 3 x 23
Step 2: Find the prime factorization of 145
145 = 5 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 20010 = 2 x 3 x 5 x 23 x 29
Step 4: Therefore, the least common multiple of 138 and 145 is 20010.