Least Common Multiple (LCM) of 107 and 179
The least common multiple (LCM) of 107 and 179 is 19153.
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 107 and 179?
First, calculate the GCD of 107 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 179 = 0 remainder 107 |
| 2 | 179 ÷ 107 = 1 remainder 72 |
| 3 | 107 ÷ 72 = 1 remainder 35 |
| 4 | 72 ÷ 35 = 2 remainder 2 |
| 5 | 35 ÷ 2 = 17 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 89 | 10947 |
| 56 and 87 | 4872 |
| 109 and 169 | 18421 |
| 168 and 149 | 25032 |
| 194 and 78 | 7566 |