Least Common Multiple (LCM) of 118 and 171
The least common multiple (LCM) of 118 and 171 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 118 and 171?
First, calculate the GCD of 118 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 171 = 0 remainder 118 |
| 2 | 171 ÷ 118 = 1 remainder 53 |
| 3 | 118 ÷ 53 = 2 remainder 12 |
| 4 | 53 ÷ 12 = 4 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 21 | 3801 |
| 114 and 200 | 11400 |
| 128 and 83 | 10624 |
| 199 and 16 | 3184 |
| 192 and 103 | 19776 |