Least Common Multiple (LCM) of 69 and 89
The least common multiple (LCM) of 69 and 89 is 6141.
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 89?
First, calculate the GCD of 69 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 89 = 0 remainder 69 |
| 2 | 89 ÷ 69 = 1 remainder 20 |
| 3 | 69 ÷ 20 = 3 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 148 | 5920 |
| 112 and 119 | 1904 |
| 41 and 54 | 2214 |
| 120 and 99 | 3960 |
| 85 and 113 | 9605 |