Least Common Multiple (LCM) of 180 and 199
The least common multiple (LCM) of 180 and 199 is 35820.
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 199?
First, calculate the GCD of 180 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 199 = 0 remainder 180 |
| 2 | 199 ÷ 180 = 1 remainder 19 |
| 3 | 180 ÷ 19 = 9 remainder 9 |
| 4 | 19 ÷ 9 = 2 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 112 | 9968 |
| 142 and 115 | 16330 |
| 96 and 70 | 3360 |
| 38 and 60 | 1140 |
| 72 and 74 | 2664 |