Least Common Multiple (LCM) of 150 and 165
The least common multiple (LCM) of 150 and 165 is 1650.
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 165?
First, calculate the GCD of 150 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 165 = 0 remainder 150 |
| 2 | 165 ÷ 150 = 1 remainder 15 |
| 3 | 150 ÷ 15 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 36 | 1476 |
| 149 and 170 | 25330 |
| 172 and 50 | 4300 |
| 165 and 110 | 330 |
| 30 and 183 | 1830 |