Least Common Multiple (LCM) of 180 and 111
The least common multiple (LCM) of 180 and 111 is 6660.
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 111?
First, calculate the GCD of 180 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 111 = 1 remainder 69 |
| 2 | 111 ÷ 69 = 1 remainder 42 |
| 3 | 69 ÷ 42 = 1 remainder 27 |
| 4 | 42 ÷ 27 = 1 remainder 15 |
| 5 | 27 ÷ 15 = 1 remainder 12 |
| 6 | 15 ÷ 12 = 1 remainder 3 |
| 7 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 99 | 1980 |
| 52 and 105 | 5460 |
| 169 and 163 | 27547 |
| 186 and 72 | 2232 |
| 36 and 126 | 252 |