Least Common Multiple (LCM) of 121 and 171
The least common multiple (LCM) of 121 and 171 is 20691.
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 121 and 171?
First, calculate the GCD of 121 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 171 = 0 remainder 121 |
| 2 | 171 ÷ 121 = 1 remainder 50 |
| 3 | 121 ÷ 50 = 2 remainder 21 |
| 4 | 50 ÷ 21 = 2 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 50 | 50 |
| 194 and 182 | 17654 |
| 160 and 157 | 25120 |
| 114 and 194 | 11058 |
| 161 and 13 | 2093 |