Least Common Multiple (LCM) of 65 and 169
The least common multiple (LCM) of 65 and 169 is 845.
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 65 and 169?
First, calculate the GCD of 65 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 169 = 0 remainder 65 |
| 2 | 169 ÷ 65 = 2 remainder 39 |
| 3 | 65 ÷ 39 = 1 remainder 26 |
| 4 | 39 ÷ 26 = 1 remainder 13 |
| 5 | 26 ÷ 13 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 16 | 400 |
| 131 and 25 | 3275 |
| 84 and 101 | 8484 |
| 127 and 20 | 2540 |
| 70 and 156 | 5460 |