Least Common Multiple (LCM) of 186 and 112
The least common multiple (LCM) of 186 and 112 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 186 and 112?
First, calculate the GCD of 186 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 112 = 1 remainder 74 |
| 2 | 112 ÷ 74 = 1 remainder 38 |
| 3 | 74 ÷ 38 = 1 remainder 36 |
| 4 | 38 ÷ 36 = 1 remainder 2 |
| 5 | 36 ÷ 2 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 53 | 3445 |
| 107 and 127 | 13589 |
| 48 and 92 | 1104 |
| 198 and 92 | 9108 |
| 37 and 178 | 6586 |