Least Common Multiple (LCM) of 150 and 177
The least common multiple (LCM) of 150 and 177 is 8850.
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 177?
First, calculate the GCD of 150 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 177 = 0 remainder 150 |
| 2 | 177 ÷ 150 = 1 remainder 27 |
| 3 | 150 ÷ 27 = 5 remainder 15 |
| 4 | 27 ÷ 15 = 1 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 33 | 1518 |
| 167 and 119 | 19873 |
| 14 and 127 | 1778 |
| 86 and 50 | 2150 |
| 100 and 61 | 6100 |