Least Common Multiple (LCM) of 112 and 186
The least common multiple (LCM) of 112 and 186 is 10416.
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 186?
First, calculate the GCD of 112 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 186 = 0 remainder 112 |
| 2 | 186 ÷ 112 = 1 remainder 74 |
| 3 | 112 ÷ 74 = 1 remainder 38 |
| 4 | 74 ÷ 38 = 1 remainder 36 |
| 5 | 38 ÷ 36 = 1 remainder 2 |
| 6 | 36 ÷ 2 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 52 | 104 |
| 113 and 94 | 10622 |
| 22 and 160 | 1760 |
| 123 and 187 | 23001 |
| 80 and 106 | 4240 |