Least Common Multiple (LCM) of 69 and 83
The least common multiple (LCM) of 69 and 83 is 5727.
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 83?
First, calculate the GCD of 69 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 83 = 0 remainder 69 |
| 2 | 83 ÷ 69 = 1 remainder 14 |
| 3 | 69 ÷ 14 = 4 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 64 | 6592 |
| 46 and 18 | 414 |
| 169 and 109 | 18421 |
| 13 and 176 | 2288 |
| 62 and 172 | 5332 |