Least Common Multiple (LCM) of 177 and 121
The least common multiple (LCM) of 177 and 121 is 21417.
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 121?
First, calculate the GCD of 177 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 121 = 1 remainder 56 |
| 2 | 121 ÷ 56 = 2 remainder 9 |
| 3 | 56 ÷ 9 = 6 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 135 | 3105 |
| 78 and 86 | 3354 |
| 47 and 84 | 3948 |
| 38 and 168 | 3192 |
| 174 and 83 | 14442 |