Least Common Multiple (LCM) of 112 and 118
The least common multiple (LCM) of 112 and 118 is 6608.
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 118?
First, calculate the GCD of 112 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 118 = 0 remainder 112 |
| 2 | 118 ÷ 112 = 1 remainder 6 |
| 3 | 112 ÷ 6 = 18 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 35 | 4760 |
| 189 and 173 | 32697 |
| 200 and 114 | 11400 |
| 20 and 36 | 180 |
| 157 and 76 | 11932 |