Least Common Multiple (LCM) of 200 and 139
The least common multiple (LCM) of 200 and 139 is 27800.
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 139?
First, calculate the GCD of 200 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 139 = 1 remainder 61 |
| 2 | 139 ÷ 61 = 2 remainder 17 |
| 3 | 61 ÷ 17 = 3 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 151 | 9815 |
| 15 and 97 | 1455 |
| 101 and 130 | 13130 |
| 130 and 66 | 4290 |
| 160 and 126 | 10080 |