Least Common Multiple (LCM) of 200 and 119
The least common multiple (LCM) of 200 and 119 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 200 and 119?
First, calculate the GCD of 200 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 119 = 1 remainder 81 |
| 2 | 119 ÷ 81 = 1 remainder 38 |
| 3 | 81 ÷ 38 = 2 remainder 5 |
| 4 | 38 ÷ 5 = 7 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 21 | 168 |
| 61 and 14 | 854 |
| 114 and 198 | 3762 |
| 138 and 35 | 4830 |
| 118 and 146 | 8614 |