Least Common Multiple (LCM) of 123 and 186
The least common multiple (LCM) of 123 and 186 is 7626.
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 186?
First, calculate the GCD of 123 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 186 = 0 remainder 123 |
| 2 | 186 ÷ 123 = 1 remainder 63 |
| 3 | 123 ÷ 63 = 1 remainder 60 |
| 4 | 63 ÷ 60 = 1 remainder 3 |
| 5 | 60 ÷ 3 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 72 | 504 |
| 109 and 102 | 11118 |
| 42 and 145 | 6090 |
| 145 and 177 | 25665 |
| 129 and 186 | 7998 |