Least Common Multiple (LCM) of 109 and 171
The least common multiple (LCM) of 109 and 171 is 18639.
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 171?
First, calculate the GCD of 109 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 171 = 0 remainder 109 |
| 2 | 171 ÷ 109 = 1 remainder 62 |
| 3 | 109 ÷ 62 = 1 remainder 47 |
| 4 | 62 ÷ 47 = 1 remainder 15 |
| 5 | 47 ÷ 15 = 3 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 80 | 560 |
| 37 and 149 | 5513 |
| 117 and 128 | 14976 |
| 183 and 81 | 4941 |
| 176 and 123 | 21648 |