Least Common Multiple (LCM) of 180 and 118
The least common multiple (LCM) of 180 and 118 is 10620.
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 118?
First, calculate the GCD of 180 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 118 = 1 remainder 62 |
| 2 | 118 ÷ 62 = 1 remainder 56 |
| 3 | 62 ÷ 56 = 1 remainder 6 |
| 4 | 56 ÷ 6 = 9 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 91 | 1638 |
| 176 and 105 | 18480 |
| 193 and 99 | 19107 |
| 84 and 147 | 588 |
| 165 and 10 | 330 |