Least Common Multiple (LCM) of 145 and 189
The least common multiple (LCM) of 145 and 189 is 27405.
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 145 and 189?
First, calculate the GCD of 145 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 189 = 0 remainder 145 |
| 2 | 189 ÷ 145 = 1 remainder 44 |
| 3 | 145 ÷ 44 = 3 remainder 13 |
| 4 | 44 ÷ 13 = 3 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 53 | 7473 |
| 114 and 155 | 17670 |
| 96 and 77 | 7392 |
| 66 and 115 | 7590 |
| 114 and 80 | 4560 |