Least Common Multiple (LCM) of 137 and 161
The least common multiple (LCM) of 137 and 161 is 22057.
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 161?
First, calculate the GCD of 137 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 161 = 0 remainder 137 |
| 2 | 161 ÷ 137 = 1 remainder 24 |
| 3 | 137 ÷ 24 = 5 remainder 17 |
| 4 | 24 ÷ 17 = 1 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 52 | 1404 |
| 164 and 133 | 21812 |
| 30 and 90 | 90 |
| 125 and 182 | 22750 |
| 44 and 122 | 2684 |