Least Common Multiple (LCM) of 177 and 115
The least common multiple (LCM) of 177 and 115 is 20355.
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 115?
First, calculate the GCD of 177 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 115 = 1 remainder 62 |
| 2 | 115 ÷ 62 = 1 remainder 53 |
| 3 | 62 ÷ 53 = 1 remainder 9 |
| 4 | 53 ÷ 9 = 5 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 60 | 540 |
| 160 and 138 | 11040 |
| 102 and 87 | 2958 |
| 138 and 170 | 11730 |
| 55 and 118 | 6490 |