Least Common Multiple (LCM) of 107 and 186
The least common multiple (LCM) of 107 and 186 is 19902.
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 107 and 186?
First, calculate the GCD of 107 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 186 = 0 remainder 107 |
| 2 | 186 ÷ 107 = 1 remainder 79 |
| 3 | 107 ÷ 79 = 1 remainder 28 |
| 4 | 79 ÷ 28 = 2 remainder 23 |
| 5 | 28 ÷ 23 = 1 remainder 5 |
| 6 | 23 ÷ 5 = 4 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 110 | 6930 |
| 22 and 103 | 2266 |
| 76 and 157 | 11932 |
| 22 and 27 | 594 |
| 32 and 138 | 2208 |