Least Common Multiple (LCM) of 189 and 56
The least common multiple (LCM) of 189 and 56 is 1512.
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 56?
First, calculate the GCD of 189 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 56 = 3 remainder 21 |
| 2 | 56 ÷ 21 = 2 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 16 | 272 |
| 92 and 199 | 18308 |
| 180 and 31 | 5580 |
| 101 and 115 | 11615 |
| 125 and 165 | 4125 |