Least Common Multiple (LCM) of 177 and 116
The least common multiple (LCM) of 177 and 116 is 20532.
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 116?
First, calculate the GCD of 177 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 116 = 1 remainder 61 |
| 2 | 116 ÷ 61 = 1 remainder 55 |
| 3 | 61 ÷ 55 = 1 remainder 6 |
| 4 | 55 ÷ 6 = 9 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 148 | 17316 |
| 59 and 145 | 8555 |
| 163 and 40 | 6520 |
| 85 and 24 | 2040 |
| 165 and 125 | 4125 |