Least Common Multiple (LCM) of 154 and 177
The least common multiple (LCM) of 154 and 177 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 154 and 177?
First, calculate the GCD of 154 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 177 = 0 remainder 154 |
| 2 | 177 ÷ 154 = 1 remainder 23 |
| 3 | 154 ÷ 23 = 6 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 17 | 1428 |
| 192 and 193 | 37056 |
| 46 and 162 | 3726 |
| 135 and 106 | 14310 |
| 54 and 71 | 3834 |