Least Common Multiple (LCM) of 121 and 170
The least common multiple (LCM) of 121 and 170 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 121 and 170?
First, calculate the GCD of 121 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 170 = 0 remainder 121 |
| 2 | 170 ÷ 121 = 1 remainder 49 |
| 3 | 121 ÷ 49 = 2 remainder 23 |
| 4 | 49 ÷ 23 = 2 remainder 3 |
| 5 | 23 ÷ 3 = 7 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 78 | 8970 |
| 194 and 180 | 17460 |
| 101 and 151 | 15251 |
| 96 and 153 | 4896 |
| 41 and 23 | 943 |