Least Common Multiple (LCM) of 177 and 119
The least common multiple (LCM) of 177 and 119 is 21063.
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 119?
First, calculate the GCD of 177 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 119 = 1 remainder 58 |
| 2 | 119 ÷ 58 = 2 remainder 3 |
| 3 | 58 ÷ 3 = 19 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 196 | 10388 |
| 75 and 188 | 14100 |
| 54 and 108 | 108 |
| 125 and 177 | 22125 |
| 83 and 22 | 1826 |