Least Common Multiple (LCM) of 180 and 116
The least common multiple (LCM) of 180 and 116 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 180 and 116?
First, calculate the GCD of 180 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 116 = 1 remainder 64 |
| 2 | 116 ÷ 64 = 1 remainder 52 |
| 3 | 64 ÷ 52 = 1 remainder 12 |
| 4 | 52 ÷ 12 = 4 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 103 | 6180 |
| 24 and 28 | 168 |
| 23 and 125 | 2875 |
| 39 and 169 | 507 |
| 130 and 189 | 24570 |