Least Common Multiple (LCM) of 180 and 200
The least common multiple (LCM) of 180 and 200 is 1800.
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 200?
First, calculate the GCD of 180 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 200 = 0 remainder 180 |
| 2 | 200 ÷ 180 = 1 remainder 20 |
| 3 | 180 ÷ 20 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 86 | 8600 |
| 48 and 164 | 1968 |
| 153 and 49 | 7497 |
| 155 and 105 | 3255 |
| 29 and 37 | 1073 |