Least Common Multiple (LCM) of 161 and 109
The least common multiple (LCM) of 161 and 109 is 17549.
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 109?
First, calculate the GCD of 161 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 161 ÷ 109 = 1 remainder 52 |
| 2 | 109 ÷ 52 = 2 remainder 5 |
| 3 | 52 ÷ 5 = 10 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 80 | 80 |
| 65 and 180 | 2340 |
| 124 and 61 | 7564 |
| 76 and 61 | 4636 |
| 179 and 124 | 22196 |