Least Common Multiple (LCM) of 113 and 179
The least common multiple (LCM) of 113 and 179 is 20227.
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 113 and 179?
First, calculate the GCD of 113 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 179 = 0 remainder 113 |
| 2 | 179 ÷ 113 = 1 remainder 66 |
| 3 | 113 ÷ 66 = 1 remainder 47 |
| 4 | 66 ÷ 47 = 1 remainder 19 |
| 5 | 47 ÷ 19 = 2 remainder 9 |
| 6 | 19 ÷ 9 = 2 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 171 | 3078 |
| 135 and 89 | 12015 |
| 160 and 133 | 21280 |
| 157 and 179 | 28103 |
| 12 and 199 | 2388 |