Least Common Multiple (LCM) of 106 and 155
The least common multiple (LCM) of 106 and 155 is 16430.
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 155?
First, calculate the GCD of 106 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 155 = 0 remainder 106 |
| 2 | 155 ÷ 106 = 1 remainder 49 |
| 3 | 106 ÷ 49 = 2 remainder 8 |
| 4 | 49 ÷ 8 = 6 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 65 | 1430 |
| 66 and 105 | 2310 |
| 75 and 177 | 4425 |
| 171 and 118 | 20178 |
| 68 and 112 | 1904 |