Least Common Multiple (LCM) of 172 and 177
The least common multiple (LCM) of 172 and 177 is 30444.
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 172 and 177?
First, calculate the GCD of 172 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 177 = 0 remainder 172 |
| 2 | 177 ÷ 172 = 1 remainder 5 |
| 3 | 172 ÷ 5 = 34 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 14 | 756 |
| 86 and 20 | 860 |
| 93 and 199 | 18507 |
| 138 and 136 | 9384 |
| 169 and 166 | 28054 |