Least Common Multiple (LCM) of 123 and 177
The least common multiple (LCM) of 123 and 177 is 7257.
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 123 and 177?
First, calculate the GCD of 123 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 177 = 0 remainder 123 |
| 2 | 177 ÷ 123 = 1 remainder 54 |
| 3 | 123 ÷ 54 = 2 remainder 15 |
| 4 | 54 ÷ 15 = 3 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 20 | 820 |
| 99 and 121 | 1089 |
| 38 and 87 | 3306 |
| 200 and 26 | 2600 |
| 123 and 141 | 5781 |