Least Common Multiple (LCM) of 69 and 104
The least common multiple (LCM) of 69 and 104 is 7176.
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 104?
First, calculate the GCD of 69 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 104 = 0 remainder 69 |
| 2 | 104 ÷ 69 = 1 remainder 35 |
| 3 | 69 ÷ 35 = 1 remainder 34 |
| 4 | 35 ÷ 34 = 1 remainder 1 |
| 5 | 34 ÷ 1 = 34 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 200 | 6600 |
| 19 and 76 | 76 |
| 197 and 88 | 17336 |
| 67 and 127 | 8509 |
| 172 and 174 | 14964 |