Least Common Multiple (LCM) of 112 and 179
The least common multiple (LCM) of 112 and 179 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 112 and 179?
First, calculate the GCD of 112 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 179 = 0 remainder 112 |
| 2 | 179 ÷ 112 = 1 remainder 67 |
| 3 | 112 ÷ 67 = 1 remainder 45 |
| 4 | 67 ÷ 45 = 1 remainder 22 |
| 5 | 45 ÷ 22 = 2 remainder 1 |
| 6 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 84 | 2688 |
| 177 and 83 | 14691 |
| 64 and 49 | 3136 |
| 36 and 105 | 1260 |
| 87 and 178 | 15486 |