Least Common Multiple (LCM) of 161 and 106
The least common multiple (LCM) of 161 and 106 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 161 and 106?
First, calculate the GCD of 161 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 161 ÷ 106 = 1 remainder 55 |
| 2 | 106 ÷ 55 = 1 remainder 51 |
| 3 | 55 ÷ 51 = 1 remainder 4 |
| 4 | 51 ÷ 4 = 12 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 44 | 7172 |
| 112 and 70 | 560 |
| 57 and 54 | 1026 |
| 110 and 176 | 880 |
| 131 and 44 | 5764 |