Least Common Multiple (LCM) of 20 and 177
The least common multiple (LCM) of 20 and 177 is 3540.
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 20 and 177?
First, calculate the GCD of 20 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 177 = 0 remainder 20 |
| 2 | 177 ÷ 20 = 8 remainder 17 |
| 3 | 20 ÷ 17 = 1 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 54 | 6534 |
| 138 and 123 | 5658 |
| 21 and 158 | 3318 |
| 112 and 83 | 9296 |
| 120 and 182 | 10920 |