Least Common Multiple of 120 and 123
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 120 and 123 the smallest integer that is 4920 that is divisible by both numbers.
Least Common Multiple (LCM) of 120 and 123 is 4920.
LCM(120,123) = 4920
LCM of 120 and 123
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 120 and 123 by Prime method
- Least Common Multiple of 120 and 123 with GCF Formula
LCM of 120 and 123 is 4920
Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 123. First we will calculate the prime factors of 120 and 123.
Prime Factorization of 120
| 2 | 120 |
| 2 | 60 |
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 120 are 2, 3,5. Prime factorization of 120 in exponential form is:
120 = 23×31×51
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
Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 123.
LCM(120,123) = 23×31×51×411
LCM(120,123) = 4920
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 123
List of positive integer factors of 123 that divides 123 without a remainder.
1, 3, 41, 123
Least Common Multiple of 120 and 123 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 120 and 123, than apply into the LCM equation.
GCF(120,123) = 3
LCM(120,123) = ( 120 × 123) / 3
LCM(120,123) = 14760 / 3
LCM(120,123) = 4920
Properties of LCM 120 and 123
(i) The LCM of 123 and 120 is associative
LCM of 120 and 123 = LCM of 123 and 120
Related Least Common Multiples of 120
Related Least Common Multiples of 123
Frequently Asked Questions on LCM of 120 and 123
1. What is the LCM of 120 and 123?
Answer: LCM of 120 and 123 is 4920.
2. What are the Factors of 120?
Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.
3. 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.
4. How to Find the LCM of 120 and 123?
Answer:
Least Common Multiple of 120 and 123 = 4920
Step 1: Find the prime factorization of 120
120 = 2 x 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 123
123 = 3 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4920 = 2 x 2 x 2 x 3 x 5 x 41
Step 4: Therefore, the least common multiple of 120 and 123 is 4920.