Least Common Multiple (LCM) of 149 and 200
The least common multiple (LCM) of 149 and 200 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 149 and 200?
First, calculate the GCD of 149 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 200 = 0 remainder 149 |
| 2 | 200 ÷ 149 = 1 remainder 51 |
| 3 | 149 ÷ 51 = 2 remainder 47 |
| 4 | 51 ÷ 47 = 1 remainder 4 |
| 5 | 47 ÷ 4 = 11 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 24 | 336 |
| 84 and 97 | 8148 |
| 95 and 35 | 665 |
| 191 and 116 | 22156 |
| 191 and 62 | 11842 |