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 |
|---|---|
| 30 and 147 | 1470 |
| 28 and 17 | 476 |
| 86 and 42 | 1806 |
| 135 and 92 | 12420 |
| 183 and 46 | 8418 |