Least Common Multiple (LCM) of 145 and 69
The least common multiple (LCM) of 145 and 69 is 10005.
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 69?
First, calculate the GCD of 145 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 69 = 2 remainder 7 |
| 2 | 69 ÷ 7 = 9 remainder 6 |
| 3 | 7 ÷ 6 = 1 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 13 | 325 |
| 116 and 186 | 10788 |
| 42 and 31 | 1302 |
| 62 and 74 | 2294 |
| 54 and 83 | 4482 |