Least Common Multiple (LCM) of 69 and 145
The least common multiple (LCM) of 69 and 145 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 69 and 145?
First, calculate the GCD of 69 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 145 = 0 remainder 69 |
| 2 | 145 ÷ 69 = 2 remainder 7 |
| 3 | 69 ÷ 7 = 9 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 97 | 10379 |
| 11 and 170 | 1870 |
| 68 and 13 | 884 |
| 99 and 81 | 891 |
| 42 and 135 | 1890 |