Least Common Multiple (LCM) of 109 and 161
The least common multiple (LCM) of 109 and 161 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 109 and 161?
First, calculate the GCD of 109 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 161 = 0 remainder 109 |
| 2 | 161 ÷ 109 = 1 remainder 52 |
| 3 | 109 ÷ 52 = 2 remainder 5 |
| 4 | 52 ÷ 5 = 10 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 87 | 10788 |
| 66 and 164 | 5412 |
| 54 and 179 | 9666 |
| 154 and 142 | 10934 |
| 27 and 49 | 1323 |