Least Common Multiple (LCM) of 123 and 180
The least common multiple (LCM) of 123 and 180 is 7380.
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 123 and 180?
First, calculate the GCD of 123 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 180 = 0 remainder 123 |
| 2 | 180 ÷ 123 = 1 remainder 57 |
| 3 | 123 ÷ 57 = 2 remainder 9 |
| 4 | 57 ÷ 9 = 6 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 118 | 8850 |
| 20 and 107 | 2140 |
| 195 and 77 | 15015 |
| 46 and 138 | 138 |
| 191 and 52 | 9932 |