Least Common Multiple (LCM) of 123 and 137
The least common multiple (LCM) of 123 and 137 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 123 and 137?
First, calculate the GCD of 123 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 137 = 0 remainder 123 |
| 2 | 137 ÷ 123 = 1 remainder 14 |
| 3 | 123 ÷ 14 = 8 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 13 | 2210 |
| 186 and 186 | 186 |
| 103 and 78 | 8034 |
| 118 and 175 | 20650 |
| 38 and 167 | 6346 |