Least Common Multiple (LCM) of 170 and 121
The least common multiple (LCM) of 170 and 121 is 20570.
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 170 and 121?
First, calculate the GCD of 170 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 121 = 1 remainder 49 |
| 2 | 121 ÷ 49 = 2 remainder 23 |
| 3 | 49 ÷ 23 = 2 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 170 | 28730 |
| 147 and 21 | 147 |
| 166 and 62 | 5146 |
| 126 and 81 | 1134 |
| 55 and 45 | 495 |