Least Common Multiple (LCM) of 120 and 123
The least common multiple (LCM) of 120 and 123 is 4920.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 120 and 123?
First, calculate the GCD of 120 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 123 = 0 remainder 120 |
| 2 | 123 ÷ 120 = 1 remainder 3 |
| 3 | 120 ÷ 3 = 40 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 129 | 7611 |
| 102 and 54 | 918 |
| 180 and 101 | 18180 |
| 121 and 112 | 13552 |
| 141 and 187 | 26367 |