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 |
|---|---|
| 37 and 69 | 2553 |
| 54 and 139 | 7506 |
| 161 and 123 | 19803 |
| 122 and 192 | 11712 |
| 73 and 36 | 2628 |