Least Common Multiple of 123 and 130
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 123 and 130 the smallest integer that is 15990 that is divisible by both numbers.
Least Common Multiple (LCM) of 123 and 130 is 15990.
LCM(123,130) = 15990
LCM of 123 and 130
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 123 and 130 by Prime method
- Least Common Multiple of 123 and 130 with GCF Formula
LCM of 123 and 130 is 15990
Least common multiple can be found by multiplying the highest exponent prime factors of 123 and 130. First we will calculate the prime factors of 123 and 130.
Prime Factorization of 123
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 123 are 3,41. Prime factorization of 123 in exponential form is:
123 = 31×411
Prime Factorization of 130
| 2 | 130 |
| 5 | 65 |
| 13 | 13 |
| 1 |
Prime factors of 130 are 2, 5,13. Prime factorization of 130 in exponential form is:
130 = 21×51×131
Now multiplying the highest exponent prime factors to calculate the LCM of 123 and 130.
LCM(123,130) = 21×31×51×131×411
LCM(123,130) = 15990
Factors of 123
List of positive integer factors of 123 that divides 123 without a remainder.
1, 3, 41, 123
Factors of 130
List of positive integer factors of 130 that divides 130 without a remainder.
1, 2, 5, 10, 13, 26, 65, 130
Least Common Multiple of 123 and 130 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 123 and 130, than apply into the LCM equation.
GCF(123,130) = 1
LCM(123,130) = ( 123 × 130) / 1
LCM(123,130) = 15990 / 1
LCM(123,130) = 15990
Properties of LCM 123 and 130
(i) The LCM of 130 and 123 is associative
LCM of 123 and 130 = LCM of 130 and 123
Related Least Common Multiples of 123
Related Least Common Multiples of 130
Frequently Asked Questions on LCM of 123 and 130
1. What is the LCM of 123 and 130?
Answer: LCM of 123 and 130 is 15990.
2. What are the Factors of 123?
Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.
3. What are the Factors of 130?
Answer: Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130. There are 8 integers that are factors of 130. The greatest factor of 130 is 130.
4. How to Find the LCM of 123 and 130?
Answer:
Least Common Multiple of 123 and 130 = 15990
Step 1: Find the prime factorization of 123
123 = 3 x 41
Step 2: Find the prime factorization of 130
130 = 2 x 5 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 15990 = 2 x 3 x 5 x 13 x 41
Step 4: Therefore, the least common multiple of 123 and 130 is 15990.
