Least Common Multiple (LCM) of 103 and 69
The least common multiple (LCM) of 103 and 69 is 7107.
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 103 and 69?
First, calculate the GCD of 103 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 69 = 1 remainder 34 |
| 2 | 69 ÷ 34 = 2 remainder 1 |
| 3 | 34 ÷ 1 = 34 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 104 | 312 |
| 171 and 156 | 8892 |
| 64 and 165 | 10560 |
| 132 and 71 | 9372 |
| 177 and 190 | 33630 |