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 |
|---|---|
| 165 and 107 | 17655 |
| 197 and 79 | 15563 |
| 155 and 73 | 11315 |
| 91 and 145 | 13195 |
| 127 and 104 | 13208 |