Least Common Multiple (LCM) of 112 and 129
The least common multiple (LCM) of 112 and 129 is 14448.
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 129?
First, calculate the GCD of 112 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 129 = 0 remainder 112 |
| 2 | 129 ÷ 112 = 1 remainder 17 |
| 3 | 112 ÷ 17 = 6 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 132 | 3036 |
| 135 and 138 | 6210 |
| 142 and 152 | 10792 |
| 38 and 151 | 5738 |
| 52 and 176 | 2288 |