Least Common Multiple (LCM) of 55 and 180
The least common multiple (LCM) of 55 and 180 is 1980.
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 55 and 180?
First, calculate the GCD of 55 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 180 = 0 remainder 55 |
| 2 | 180 ÷ 55 = 3 remainder 15 |
| 3 | 55 ÷ 15 = 3 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 130 | 14430 |
| 146 and 146 | 146 |
| 159 and 140 | 22260 |
| 29 and 109 | 3161 |
| 100 and 119 | 11900 |