Least Common Multiple (LCM) of 29 and 112
The least common multiple (LCM) of 29 and 112 is 3248.
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 29 and 112?
First, calculate the GCD of 29 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 112 = 0 remainder 29 |
| 2 | 112 ÷ 29 = 3 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 155 | 930 |
| 161 and 166 | 26726 |
| 134 and 14 | 938 |
| 85 and 121 | 10285 |
| 154 and 113 | 17402 |