Least Common Multiple (LCM) of 114 and 179
The least common multiple (LCM) of 114 and 179 is 20406.
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 114 and 179?
First, calculate the GCD of 114 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 179 = 0 remainder 114 |
| 2 | 179 ÷ 114 = 1 remainder 65 |
| 3 | 114 ÷ 65 = 1 remainder 49 |
| 4 | 65 ÷ 49 = 1 remainder 16 |
| 5 | 49 ÷ 16 = 3 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 185 | 24605 |
| 175 and 124 | 21700 |
| 127 and 75 | 9525 |
| 86 and 30 | 1290 |
| 177 and 123 | 7257 |