Least Common Multiple (LCM) of 109 and 179
The least common multiple (LCM) of 109 and 179 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 109 and 179?
First, calculate the GCD of 109 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 179 = 0 remainder 109 |
| 2 | 179 ÷ 109 = 1 remainder 70 |
| 3 | 109 ÷ 70 = 1 remainder 39 |
| 4 | 70 ÷ 39 = 1 remainder 31 |
| 5 | 39 ÷ 31 = 1 remainder 8 |
| 6 | 31 ÷ 8 = 3 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 60 | 120 |
| 45 and 111 | 1665 |
| 144 and 79 | 11376 |
| 95 and 93 | 8835 |
| 159 and 61 | 9699 |