Least Common Multiple (LCM) of 188 and 107
The least common multiple (LCM) of 188 and 107 is 20116.
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 188 and 107?
First, calculate the GCD of 188 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 107 = 1 remainder 81 |
| 2 | 107 ÷ 81 = 1 remainder 26 |
| 3 | 81 ÷ 26 = 3 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 147 | 16611 |
| 140 and 185 | 5180 |
| 92 and 133 | 12236 |
| 171 and 151 | 25821 |
| 192 and 30 | 960 |