Least Common Multiple (LCM) of 115 and 186
The least common multiple (LCM) of 115 and 186 is 21390.
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 115 and 186?
First, calculate the GCD of 115 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 186 = 0 remainder 115 |
| 2 | 186 ÷ 115 = 1 remainder 71 |
| 3 | 115 ÷ 71 = 1 remainder 44 |
| 4 | 71 ÷ 44 = 1 remainder 27 |
| 5 | 44 ÷ 27 = 1 remainder 17 |
| 6 | 27 ÷ 17 = 1 remainder 10 |
| 7 | 17 ÷ 10 = 1 remainder 7 |
| 8 | 10 ÷ 7 = 1 remainder 3 |
| 9 | 7 ÷ 3 = 2 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 173 | 6055 |
| 144 and 27 | 432 |
| 129 and 72 | 3096 |
| 130 and 97 | 12610 |
| 120 and 70 | 840 |