Least Common Multiple (LCM) of 200 and 149
The least common multiple (LCM) of 200 and 149 is 29800.
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 149?
First, calculate the GCD of 200 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 149 = 1 remainder 51 |
| 2 | 149 ÷ 51 = 2 remainder 47 |
| 3 | 51 ÷ 47 = 1 remainder 4 |
| 4 | 47 ÷ 4 = 11 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 43 | 4773 |
| 113 and 126 | 14238 |
| 117 and 44 | 5148 |
| 56 and 165 | 9240 |
| 134 and 112 | 7504 |