Least Common Multiple (LCM) of 116 and 180
The least common multiple (LCM) of 116 and 180 is 5220.
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 116 and 180?
First, calculate the GCD of 116 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 180 = 0 remainder 116 |
| 2 | 180 ÷ 116 = 1 remainder 64 |
| 3 | 116 ÷ 64 = 1 remainder 52 |
| 4 | 64 ÷ 52 = 1 remainder 12 |
| 5 | 52 ÷ 12 = 4 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 31 | 3782 |
| 27 and 114 | 1026 |
| 186 and 43 | 7998 |
| 63 and 183 | 3843 |
| 24 and 183 | 1464 |