Least Common Multiple (LCM) of 106 and 187
The least common multiple (LCM) of 106 and 187 is 19822.
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 106 and 187?
First, calculate the GCD of 106 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 187 = 0 remainder 106 |
| 2 | 187 ÷ 106 = 1 remainder 81 |
| 3 | 106 ÷ 81 = 1 remainder 25 |
| 4 | 81 ÷ 25 = 3 remainder 6 |
| 5 | 25 ÷ 6 = 4 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 82 | 14022 |
| 110 and 51 | 5610 |
| 194 and 36 | 3492 |
| 36 and 157 | 5652 |
| 54 and 114 | 1026 |