Least Common Multiple (LCM) of 179 and 109
The least common multiple (LCM) of 179 and 109 is 19511.
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 109?
First, calculate the GCD of 179 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 109 = 1 remainder 70 |
| 2 | 109 ÷ 70 = 1 remainder 39 |
| 3 | 70 ÷ 39 = 1 remainder 31 |
| 4 | 39 ÷ 31 = 1 remainder 8 |
| 5 | 31 ÷ 8 = 3 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 177 | 9735 |
| 130 and 103 | 13390 |
| 113 and 200 | 22600 |
| 198 and 102 | 3366 |
| 153 and 15 | 765 |