Least Common Multiple (LCM) of 171 and 119
The least common multiple (LCM) of 171 and 119 is 20349.
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 171 and 119?
First, calculate the GCD of 171 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 119 = 1 remainder 52 |
| 2 | 119 ÷ 52 = 2 remainder 15 |
| 3 | 52 ÷ 15 = 3 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 98 | 1470 |
| 17 and 17 | 17 |
| 140 and 49 | 980 |
| 96 and 81 | 2592 |
| 165 and 91 | 15015 |