Least Common Multiple of 138 and 139
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 139 the smallest integer that is 19182 that is divisible by both numbers.
Least Common Multiple (LCM) of 138 and 139 is 19182.
LCM(138,139) = 19182
LCM of 138 and 139
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 138 and 139 by Prime method
- Least Common Multiple of 138 and 139 with GCF Formula
LCM of 138 and 139 is 19182
Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 139. First we will calculate the prime factors of 138 and 139.
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 139
| 139 | 139 |
| 1 |
Prime factors of 139 are 139. Prime factorization of 139 in exponential form is:
139 = 1391
Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 139.
LCM(138,139) = 21×31×231×1391
LCM(138,139) = 19182
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 139
List of positive integer factors of 139 that divides 139 without a remainder.
1, 139
Least Common Multiple of 138 and 139 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 139, than apply into the LCM equation.
GCF(138,139) = 1
LCM(138,139) = ( 138 × 139) / 1
LCM(138,139) = 19182 / 1
LCM(138,139) = 19182
Properties of LCM 138 and 139
(i) The LCM of 139 and 138 is associative
LCM of 138 and 139 = LCM of 139 and 138
Related Least Common Multiples of 138
Related Least Common Multiples of 139
Frequently Asked Questions on LCM of 138 and 139
1. What is the LCM of 138 and 139?
Answer: LCM of 138 and 139 is 19182.
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 139?
Answer: Factors of 139 are 1, 139. There are 2 integers that are factors of 139. The greatest factor of 139 is 139.
4. How to Find the LCM of 138 and 139?
Answer:
Least Common Multiple of 138 and 139 = 19182
Step 1: Find the prime factorization of 138
138 = 2 x 3 x 23
Step 2: Find the prime factorization of 139
139 = 139
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 19182 = 2 x 3 x 23 x 139
Step 4: Therefore, the least common multiple of 138 and 139 is 19182.
