Least Common Multiple (LCM) of 117 and 180
The least common multiple (LCM) of 117 and 180 is 2340.
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 180?
First, calculate the GCD of 117 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 180 = 0 remainder 117 |
| 2 | 180 ÷ 117 = 1 remainder 63 |
| 3 | 117 ÷ 63 = 1 remainder 54 |
| 4 | 63 ÷ 54 = 1 remainder 9 |
| 5 | 54 ÷ 9 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 68 | 3740 |
| 166 and 163 | 27058 |
| 180 and 69 | 4140 |
| 73 and 130 | 9490 |
| 27 and 199 | 5373 |