Least Common Multiple (LCM) of 144 and 200
The least common multiple (LCM) of 144 and 200 is 3600.
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 144 and 200?
First, calculate the GCD of 144 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 200 = 0 remainder 144 |
| 2 | 200 ÷ 144 = 1 remainder 56 |
| 3 | 144 ÷ 56 = 2 remainder 32 |
| 4 | 56 ÷ 32 = 1 remainder 24 |
| 5 | 32 ÷ 24 = 1 remainder 8 |
| 6 | 24 ÷ 8 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 189 | 9450 |
| 37 and 59 | 2183 |
| 109 and 170 | 18530 |
| 83 and 89 | 7387 |
| 14 and 122 | 854 |