Least Common Multiple (LCM) of 109 and 188
The least common multiple (LCM) of 109 and 188 is 20492.
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 109 and 188?
First, calculate the GCD of 109 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 188 = 0 remainder 109 |
| 2 | 188 ÷ 109 = 1 remainder 79 |
| 3 | 109 ÷ 79 = 1 remainder 30 |
| 4 | 79 ÷ 30 = 2 remainder 19 |
| 5 | 30 ÷ 19 = 1 remainder 11 |
| 6 | 19 ÷ 11 = 1 remainder 8 |
| 7 | 11 ÷ 8 = 1 remainder 3 |
| 8 | 8 ÷ 3 = 2 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 162 | 162 |
| 158 and 172 | 13588 |
| 104 and 123 | 12792 |
| 134 and 21 | 2814 |
| 15 and 55 | 165 |