Least Common Multiple (LCM) of 112 and 188
The least common multiple (LCM) of 112 and 188 is 5264.
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 188?
First, calculate the GCD of 112 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 188 = 0 remainder 112 |
| 2 | 188 ÷ 112 = 1 remainder 76 |
| 3 | 112 ÷ 76 = 1 remainder 36 |
| 4 | 76 ÷ 36 = 2 remainder 4 |
| 5 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 88 | 1584 |
| 70 and 133 | 1330 |
| 30 and 197 | 5910 |
| 115 and 179 | 20585 |
| 182 and 192 | 17472 |