Least Common Multiple (LCM) of 108 and 186
The least common multiple (LCM) of 108 and 186 is 3348.
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 108 and 186?
First, calculate the GCD of 108 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 186 = 0 remainder 108 |
| 2 | 186 ÷ 108 = 1 remainder 78 |
| 3 | 108 ÷ 78 = 1 remainder 30 |
| 4 | 78 ÷ 30 = 2 remainder 18 |
| 5 | 30 ÷ 18 = 1 remainder 12 |
| 6 | 18 ÷ 12 = 1 remainder 6 |
| 7 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 41 | 6642 |
| 52 and 106 | 2756 |
| 198 and 17 | 3366 |
| 37 and 136 | 5032 |
| 129 and 82 | 10578 |