Least Common Multiple (LCM) of 123 and 146
The least common multiple (LCM) of 123 and 146 is 17958.
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 146?
First, calculate the GCD of 123 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 146 = 0 remainder 123 |
| 2 | 146 ÷ 123 = 1 remainder 23 |
| 3 | 123 ÷ 23 = 5 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 157 | 12246 |
| 114 and 62 | 3534 |
| 199 and 115 | 22885 |
| 36 and 22 | 396 |
| 49 and 149 | 7301 |