Least Common Multiple (LCM) of 105 and 188
The least common multiple (LCM) of 105 and 188 is 19740.
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 105 and 188?
First, calculate the GCD of 105 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 188 = 0 remainder 105 |
| 2 | 188 ÷ 105 = 1 remainder 83 |
| 3 | 105 ÷ 83 = 1 remainder 22 |
| 4 | 83 ÷ 22 = 3 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 80 | 6480 |
| 136 and 198 | 13464 |
| 163 and 135 | 22005 |
| 172 and 65 | 11180 |
| 108 and 32 | 864 |