Least Common Multiple (LCM) of 40 and 189
The least common multiple (LCM) of 40 and 189 is 7560.
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 40 and 189?
First, calculate the GCD of 40 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 189 = 0 remainder 40 |
| 2 | 189 ÷ 40 = 4 remainder 29 |
| 3 | 40 ÷ 29 = 1 remainder 11 |
| 4 | 29 ÷ 11 = 2 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 174 | 23838 |
| 159 and 28 | 4452 |
| 105 and 70 | 210 |
| 46 and 200 | 4600 |
| 171 and 112 | 19152 |