Least Common Multiple (LCM) of 177 and 77
The least common multiple (LCM) of 177 and 77 is 13629.
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 77?
First, calculate the GCD of 177 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 77 = 2 remainder 23 |
| 2 | 77 ÷ 23 = 3 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 89 | 10146 |
| 64 and 119 | 7616 |
| 156 and 23 | 3588 |
| 174 and 12 | 348 |
| 165 and 89 | 14685 |