Least Common Multiple (LCM) of 112 and 55
The least common multiple (LCM) of 112 and 55 is 6160.
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 55?
First, calculate the GCD of 112 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 55 = 2 remainder 2 |
| 2 | 55 ÷ 2 = 27 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 132 | 8052 |
| 18 and 11 | 198 |
| 12 and 116 | 348 |
| 44 and 21 | 924 |
| 77 and 133 | 1463 |