Least Common Multiple (LCM) of 200 and 39
The least common multiple (LCM) of 200 and 39 is 7800.
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 39?
First, calculate the GCD of 200 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 39 = 5 remainder 5 |
| 2 | 39 ÷ 5 = 7 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 39 | 6123 |
| 133 and 11 | 1463 |
| 41 and 59 | 2419 |
| 19 and 150 | 2850 |
| 54 and 23 | 1242 |