Least Common Multiple (LCM) of 179 and 108
The least common multiple (LCM) of 179 and 108 is 19332.
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 179 and 108?
First, calculate the GCD of 179 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 108 = 1 remainder 71 |
| 2 | 108 ÷ 71 = 1 remainder 37 |
| 3 | 71 ÷ 37 = 1 remainder 34 |
| 4 | 37 ÷ 34 = 1 remainder 3 |
| 5 | 34 ÷ 3 = 11 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 37 | 3293 |
| 44 and 146 | 3212 |
| 54 and 108 | 108 |
| 117 and 108 | 1404 |
| 103 and 133 | 13699 |