Least Common Multiple (LCM) of 106 and 186
The least common multiple (LCM) of 106 and 186 is 9858.
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 106 and 186?
First, calculate the GCD of 106 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 186 = 0 remainder 106 |
| 2 | 186 ÷ 106 = 1 remainder 80 |
| 3 | 106 ÷ 80 = 1 remainder 26 |
| 4 | 80 ÷ 26 = 3 remainder 2 |
| 5 | 26 ÷ 2 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 128 | 12672 |
| 124 and 60 | 1860 |
| 83 and 21 | 1743 |
| 15 and 93 | 465 |
| 199 and 173 | 34427 |