Least Common Multiple (LCM) of 112 and 195
The least common multiple (LCM) of 112 and 195 is 21840.
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 195?
First, calculate the GCD of 112 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 195 = 0 remainder 112 |
| 2 | 195 ÷ 112 = 1 remainder 83 |
| 3 | 112 ÷ 83 = 1 remainder 29 |
| 4 | 83 ÷ 29 = 2 remainder 25 |
| 5 | 29 ÷ 25 = 1 remainder 4 |
| 6 | 25 ÷ 4 = 6 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 180 | 720 |
| 121 and 55 | 605 |
| 133 and 118 | 15694 |
| 146 and 51 | 7446 |
| 46 and 93 | 4278 |