Least Common Multiple (LCM) of 137 and 115
The least common multiple (LCM) of 137 and 115 is 15755.
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 115?
First, calculate the GCD of 137 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 115 = 1 remainder 22 |
| 2 | 115 ÷ 22 = 5 remainder 5 |
| 3 | 22 ÷ 5 = 4 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 158 | 14062 |
| 155 and 148 | 22940 |
| 19 and 173 | 3287 |
| 129 and 108 | 4644 |
| 111 and 127 | 14097 |