Least Common Multiple (LCM) of 189 and 112
The least common multiple (LCM) of 189 and 112 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 189 and 112?
First, calculate the GCD of 189 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 112 = 1 remainder 77 |
| 2 | 112 ÷ 77 = 1 remainder 35 |
| 3 | 77 ÷ 35 = 2 remainder 7 |
| 4 | 35 ÷ 7 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 54 | 3780 |
| 24 and 94 | 1128 |
| 149 and 93 | 13857 |
| 164 and 59 | 9676 |
| 106 and 124 | 6572 |