Least Common Multiple (LCM) of 112 and 189
The least common multiple (LCM) of 112 and 189 is 3024.
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 189?
First, calculate the GCD of 112 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 189 = 0 remainder 112 |
| 2 | 189 ÷ 112 = 1 remainder 77 |
| 3 | 112 ÷ 77 = 1 remainder 35 |
| 4 | 77 ÷ 35 = 2 remainder 7 |
| 5 | 35 ÷ 7 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 10 | 780 |
| 185 and 148 | 740 |
| 35 and 145 | 1015 |
| 106 and 176 | 9328 |
| 148 and 71 | 10508 |