Least Common Multiple (LCM) of 105 and 161
The least common multiple (LCM) of 105 and 161 is 2415.
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 105 and 161?
First, calculate the GCD of 105 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 161 = 0 remainder 105 |
| 2 | 161 ÷ 105 = 1 remainder 56 |
| 3 | 105 ÷ 56 = 1 remainder 49 |
| 4 | 56 ÷ 49 = 1 remainder 7 |
| 5 | 49 ÷ 7 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 130 | 2730 |
| 171 and 114 | 342 |
| 168 and 105 | 840 |
| 121 and 164 | 19844 |
| 67 and 112 | 7504 |