Least Common Multiple (LCM) of 117 and 171
The least common multiple (LCM) of 117 and 171 is 2223.
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 117 and 171?
First, calculate the GCD of 117 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 171 = 0 remainder 117 |
| 2 | 171 ÷ 117 = 1 remainder 54 |
| 3 | 117 ÷ 54 = 2 remainder 9 |
| 4 | 54 ÷ 9 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 81 | 15957 |
| 48 and 113 | 5424 |
| 56 and 111 | 6216 |
| 38 and 200 | 3800 |
| 139 and 113 | 15707 |