Least Common Multiple (LCM) of 180 and 113
The least common multiple (LCM) of 180 and 113 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 180 and 113?
First, calculate the GCD of 180 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 113 = 1 remainder 67 |
| 2 | 113 ÷ 67 = 1 remainder 46 |
| 3 | 67 ÷ 46 = 1 remainder 21 |
| 4 | 46 ÷ 21 = 2 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 76 | 76 |
| 42 and 163 | 6846 |
| 129 and 19 | 2451 |
| 88 and 122 | 5368 |
| 186 and 160 | 14880 |