Least Common Multiple (LCM) of 123 and 189
The least common multiple (LCM) of 123 and 189 is 7749.
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 189?
First, calculate the GCD of 123 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 189 = 0 remainder 123 |
| 2 | 189 ÷ 123 = 1 remainder 66 |
| 3 | 123 ÷ 66 = 1 remainder 57 |
| 4 | 66 ÷ 57 = 1 remainder 9 |
| 5 | 57 ÷ 9 = 6 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 135 | 16065 |
| 39 and 86 | 3354 |
| 169 and 109 | 18421 |
| 13 and 73 | 949 |
| 118 and 145 | 17110 |