Least Common Multiple (LCM) of 106 and 171
The least common multiple (LCM) of 106 and 171 is 18126.
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 171?
First, calculate the GCD of 106 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 171 = 0 remainder 106 |
| 2 | 171 ÷ 106 = 1 remainder 65 |
| 3 | 106 ÷ 65 = 1 remainder 41 |
| 4 | 65 ÷ 41 = 1 remainder 24 |
| 5 | 41 ÷ 24 = 1 remainder 17 |
| 6 | 24 ÷ 17 = 1 remainder 7 |
| 7 | 17 ÷ 7 = 2 remainder 3 |
| 8 | 7 ÷ 3 = 2 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 18 | 1530 |
| 162 and 114 | 3078 |
| 96 and 150 | 2400 |
| 84 and 25 | 2100 |
| 181 and 141 | 25521 |