Least Common Multiple (LCM) of 171 and 118
The least common multiple (LCM) of 171 and 118 is 20178.
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 118?
First, calculate the GCD of 171 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 118 = 1 remainder 53 |
| 2 | 118 ÷ 53 = 2 remainder 12 |
| 3 | 53 ÷ 12 = 4 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 29 | 2552 |
| 70 and 105 | 210 |
| 81 and 134 | 10854 |
| 123 and 52 | 6396 |
| 96 and 18 | 288 |