Least Common Multiple (LCM) of 157 and 177
The least common multiple (LCM) of 157 and 177 is 27789.
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 157 and 177?
First, calculate the GCD of 157 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 177 = 0 remainder 157 |
| 2 | 177 ÷ 157 = 1 remainder 20 |
| 3 | 157 ÷ 20 = 7 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 133 | 8778 |
| 180 and 199 | 35820 |
| 46 and 185 | 8510 |
| 147 and 178 | 26166 |
| 93 and 158 | 14694 |