Least Common Multiple (LCM) of 119 and 200
The least common multiple (LCM) of 119 and 200 is 23800.
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 119 and 200?
First, calculate the GCD of 119 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 200 = 0 remainder 119 |
| 2 | 200 ÷ 119 = 1 remainder 81 |
| 3 | 119 ÷ 81 = 1 remainder 38 |
| 4 | 81 ÷ 38 = 2 remainder 5 |
| 5 | 38 ÷ 5 = 7 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 53 | 7367 |
| 186 and 50 | 4650 |
| 36 and 75 | 900 |
| 140 and 113 | 15820 |
| 20 and 57 | 1140 |