Least Common Multiple (LCM) of 177 and 45
The least common multiple (LCM) of 177 and 45 is 2655.
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 45?
First, calculate the GCD of 177 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 45 = 3 remainder 42 |
| 2 | 45 ÷ 42 = 1 remainder 3 |
| 3 | 42 ÷ 3 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 97 | 9700 |
| 153 and 112 | 17136 |
| 19 and 111 | 2109 |
| 112 and 101 | 11312 |
| 144 and 103 | 14832 |