Least Common Multiple (LCM) of 111 and 180
The least common multiple (LCM) of 111 and 180 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 111 and 180?
First, calculate the GCD of 111 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 180 = 0 remainder 111 |
| 2 | 180 ÷ 111 = 1 remainder 69 |
| 3 | 111 ÷ 69 = 1 remainder 42 |
| 4 | 69 ÷ 42 = 1 remainder 27 |
| 5 | 42 ÷ 27 = 1 remainder 15 |
| 6 | 27 ÷ 15 = 1 remainder 12 |
| 7 | 15 ÷ 12 = 1 remainder 3 |
| 8 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 33 | 165 |
| 126 and 51 | 2142 |
| 70 and 105 | 210 |
| 169 and 50 | 8450 |
| 14 and 10 | 70 |