Least Common Multiple (LCM) of 121 and 177
The least common multiple (LCM) of 121 and 177 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 121 and 177?
First, calculate the GCD of 121 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 177 = 0 remainder 121 |
| 2 | 177 ÷ 121 = 1 remainder 56 |
| 3 | 121 ÷ 56 = 2 remainder 9 |
| 4 | 56 ÷ 9 = 6 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 112 | 1680 |
| 82 and 186 | 7626 |
| 106 and 16 | 848 |
| 80 and 10 | 80 |
| 49 and 84 | 588 |