Least Common Multiple (LCM) of 55 and 186
The least common multiple (LCM) of 55 and 186 is 10230.
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 55 and 186?
First, calculate the GCD of 55 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 186 = 0 remainder 55 |
| 2 | 186 ÷ 55 = 3 remainder 21 |
| 3 | 55 ÷ 21 = 2 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 179 | 25239 |
| 84 and 66 | 924 |
| 82 and 37 | 3034 |
| 190 and 167 | 31730 |
| 82 and 144 | 5904 |