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 |
|---|---|
| 65 and 178 | 11570 |
| 31 and 88 | 2728 |
| 80 and 45 | 720 |
| 81 and 126 | 1134 |
| 137 and 173 | 23701 |