Least Common Multiple (LCM) of 119 and 177
The least common multiple (LCM) of 119 and 177 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 119 and 177?
First, calculate the GCD of 119 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 177 = 0 remainder 119 |
| 2 | 177 ÷ 119 = 1 remainder 58 |
| 3 | 119 ÷ 58 = 2 remainder 3 |
| 4 | 58 ÷ 3 = 19 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 137 | 22468 |
| 82 and 86 | 3526 |
| 80 and 151 | 12080 |
| 129 and 129 | 129 |
| 132 and 85 | 11220 |