Least Common Multiple of 138 and 145
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 138 and 145 the smallest integer that is 20010 that is divisible by both numbers.
Least Common Multiple (LCM) of 138 and 145 is 20010.
LCM(138,145) = 20010
LCM of 138 and 145
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 138 and 145 by Prime method
- Least Common Multiple of 138 and 145 with GCF Formula
LCM of 138 and 145 is 20010
Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 145. First we will calculate the prime factors of 138 and 145.
Prime Factorization of 138
| 2 | 138 |
| 3 | 69 |
| 23 | 23 |
| 1 |
Prime factors of 138 are 2, 3,23. Prime factorization of 138 in exponential form is:
138 = 21×31×231
Prime Factorization of 145
| 5 | 145 |
| 29 | 29 |
| 1 |
Prime factors of 145 are 5,29. Prime factorization of 145 in exponential form is:
145 = 51×291
Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 145.
LCM(138,145) = 21×31×51×231×291
LCM(138,145) = 20010
Factors of 138
List of positive integer factors of 138 that divides 138 without a remainder.
1, 2, 3, 6, 23, 46, 69, 138
Factors of 145
List of positive integer factors of 145 that divides 145 without a remainder.
1, 5, 29, 145
Least Common Multiple of 138 and 145 with GCF Formula
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
Properties of LCM 138 and 145
(i) The LCM of 145 and 138 is associative
LCM of 138 and 145 = LCM of 145 and 138
Related Least Common Multiples of 138
Related Least Common Multiples of 145
Frequently Asked Questions on LCM of 138 and 145
1. What is the LCM of 138 and 145?
Answer: LCM of 138 and 145 is 20010.
2. 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.
3. 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.
4. 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.
