Least Common Multiple (LCM) of 179 and 112
The least common multiple (LCM) of 179 and 112 is 20048.
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 112?
First, calculate the GCD of 179 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 112 = 1 remainder 67 |
| 2 | 112 ÷ 67 = 1 remainder 45 |
| 3 | 67 ÷ 45 = 1 remainder 22 |
| 4 | 45 ÷ 22 = 2 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 166 | 15604 |
| 102 and 48 | 816 |
| 164 and 163 | 26732 |
| 31 and 93 | 93 |
| 99 and 73 | 7227 |