Least Common Multiple (LCM) of 189 and 40
The least common multiple (LCM) of 189 and 40 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 189 and 40?
First, calculate the GCD of 189 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 40 = 4 remainder 29 |
| 2 | 40 ÷ 29 = 1 remainder 11 |
| 3 | 29 ÷ 11 = 2 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 64 | 1216 |
| 107 and 83 | 8881 |
| 50 and 59 | 2950 |
| 60 and 85 | 1020 |
| 136 and 117 | 15912 |