Least Common Multiple (LCM) of 61 and 177
The least common multiple (LCM) of 61 and 177 is 10797.
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 61 and 177?
First, calculate the GCD of 61 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 177 = 0 remainder 61 |
| 2 | 177 ÷ 61 = 2 remainder 55 |
| 3 | 61 ÷ 55 = 1 remainder 6 |
| 4 | 55 ÷ 6 = 9 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 13 | 2574 |
| 13 and 60 | 780 |
| 145 and 55 | 1595 |
| 52 and 180 | 2340 |
| 113 and 31 | 3503 |