Least Common Multiple (LCM) of 106 and 161
The least common multiple (LCM) of 106 and 161 is 17066.
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 161?
First, calculate the GCD of 106 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 161 = 0 remainder 106 |
| 2 | 161 ÷ 106 = 1 remainder 55 |
| 3 | 106 ÷ 55 = 1 remainder 51 |
| 4 | 55 ÷ 51 = 1 remainder 4 |
| 5 | 51 ÷ 4 = 12 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 186 | 5022 |
| 65 and 153 | 9945 |
| 160 and 68 | 2720 |
| 55 and 172 | 9460 |
| 38 and 23 | 874 |