Least Common Multiple (LCM) of 114 and 177
The least common multiple (LCM) of 114 and 177 is 6726.
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 114 and 177?
First, calculate the GCD of 114 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 177 = 0 remainder 114 |
| 2 | 177 ÷ 114 = 1 remainder 63 |
| 3 | 114 ÷ 63 = 1 remainder 51 |
| 4 | 63 ÷ 51 = 1 remainder 12 |
| 5 | 51 ÷ 12 = 4 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 122 | 12078 |
| 54 and 34 | 918 |
| 77 and 24 | 1848 |
| 31 and 116 | 3596 |
| 110 and 169 | 18590 |