Least Common Multiple (LCM) of 137 and 177
The least common multiple (LCM) of 137 and 177 is 24249.
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 177?
First, calculate the GCD of 137 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 177 = 0 remainder 137 |
| 2 | 177 ÷ 137 = 1 remainder 40 |
| 3 | 137 ÷ 40 = 3 remainder 17 |
| 4 | 40 ÷ 17 = 2 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 137 | 16577 |
| 180 and 116 | 5220 |
| 164 and 125 | 20500 |
| 97 and 121 | 11737 |
| 84 and 22 | 924 |