Least Common Multiple (LCM) of 189 and 150
The least common multiple (LCM) of 189 and 150 is 9450.
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 189 and 150?
First, calculate the GCD of 189 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 150 = 1 remainder 39 |
| 2 | 150 ÷ 39 = 3 remainder 33 |
| 3 | 39 ÷ 33 = 1 remainder 6 |
| 4 | 33 ÷ 6 = 5 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 157 | 28417 |
| 106 and 157 | 16642 |
| 175 and 48 | 8400 |
| 88 and 179 | 15752 |
| 21 and 198 | 1386 |