Least Common Multiple (LCM) of 113 and 180
The least common multiple (LCM) of 113 and 180 is 20340.
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 113 and 180?
First, calculate the GCD of 113 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 180 = 0 remainder 113 |
| 2 | 180 ÷ 113 = 1 remainder 67 |
| 3 | 113 ÷ 67 = 1 remainder 46 |
| 4 | 67 ÷ 46 = 1 remainder 21 |
| 5 | 46 ÷ 21 = 2 remainder 4 |
| 6 | 21 ÷ 4 = 5 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 67 | 5695 |
| 148 and 198 | 14652 |
| 73 and 86 | 6278 |
| 55 and 78 | 4290 |
| 158 and 70 | 5530 |