Least Common Multiple (LCM) of 177 and 154
The least common multiple (LCM) of 177 and 154 is 27258.
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 177 and 154?
First, calculate the GCD of 177 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 154 = 1 remainder 23 |
| 2 | 154 ÷ 23 = 6 remainder 16 |
| 3 | 23 ÷ 16 = 1 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 127 | 3429 |
| 142 and 71 | 142 |
| 20 and 177 | 3540 |
| 66 and 123 | 2706 |
| 17 and 48 | 816 |