Least Common Multiple (LCM) of 180 and 117
The least common multiple (LCM) of 180 and 117 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 180 and 117?
First, calculate the GCD of 180 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 117 = 1 remainder 63 |
| 2 | 117 ÷ 63 = 1 remainder 54 |
| 3 | 63 ÷ 54 = 1 remainder 9 |
| 4 | 54 ÷ 9 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 34 | 2550 |
| 194 and 97 | 194 |
| 99 and 181 | 17919 |
| 57 and 59 | 3363 |
| 126 and 25 | 3150 |