Least Common Multiple (LCM) of 112 and 34
The least common multiple (LCM) of 112 and 34 is 1904.
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 34?
First, calculate the GCD of 112 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 34 = 3 remainder 10 |
| 2 | 34 ÷ 10 = 3 remainder 4 |
| 3 | 10 ÷ 4 = 2 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 87 | 7482 |
| 31 and 142 | 4402 |
| 192 and 140 | 6720 |
| 139 and 161 | 22379 |
| 153 and 147 | 7497 |