Least Common Multiple (LCM) of 137 and 163
The least common multiple (LCM) of 137 and 163 is 22331.
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 163?
First, calculate the GCD of 137 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 163 = 0 remainder 137 |
| 2 | 163 ÷ 137 = 1 remainder 26 |
| 3 | 137 ÷ 26 = 5 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 198 | 27126 |
| 76 and 136 | 2584 |
| 65 and 89 | 5785 |
| 167 and 39 | 6513 |
| 183 and 126 | 7686 |