Least Common Multiple (LCM) of 200 and 144
The least common multiple (LCM) of 200 and 144 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 200 and 144?
First, calculate the GCD of 200 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 144 = 1 remainder 56 |
| 2 | 144 ÷ 56 = 2 remainder 32 |
| 3 | 56 ÷ 32 = 1 remainder 24 |
| 4 | 32 ÷ 24 = 1 remainder 8 |
| 5 | 24 ÷ 8 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 10 | 90 |
| 62 and 101 | 6262 |
| 140 and 11 | 1540 |
| 182 and 99 | 18018 |
| 44 and 23 | 1012 |