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 |
|---|---|
| 156 and 49 | 7644 |
| 10 and 45 | 90 |
| 157 and 22 | 3454 |
| 141 and 164 | 23124 |
| 111 and 98 | 10878 |