Least Common Multiple (LCM) of 137 and 123
The least common multiple (LCM) of 137 and 123 is 16851.
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 137 and 123?
First, calculate the GCD of 137 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 123 = 1 remainder 14 |
| 2 | 123 ÷ 14 = 8 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 121 | 13794 |
| 117 and 33 | 1287 |
| 34 and 25 | 850 |
| 137 and 109 | 14933 |
| 75 and 89 | 6675 |