Least Common Multiple (LCM) of 77 and 177
The least common multiple (LCM) of 77 and 177 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 77 and 177?
First, calculate the GCD of 77 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 177 = 0 remainder 77 |
| 2 | 177 ÷ 77 = 2 remainder 23 |
| 3 | 77 ÷ 23 = 3 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 166 | 6308 |
| 105 and 59 | 6195 |
| 172 and 194 | 16684 |
| 160 and 79 | 12640 |
| 148 and 156 | 5772 |