Least Common Multiple (LCM) of 150 and 199
The least common multiple (LCM) of 150 and 199 is 29850.
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 150 and 199?
First, calculate the GCD of 150 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 199 = 0 remainder 150 |
| 2 | 199 ÷ 150 = 1 remainder 49 |
| 3 | 150 ÷ 49 = 3 remainder 3 |
| 4 | 49 ÷ 3 = 16 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 78 | 1326 |
| 85 and 120 | 2040 |
| 121 and 48 | 5808 |
| 178 and 184 | 16376 |
| 156 and 156 | 156 |