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 |
|---|---|
| 140 and 34 | 2380 |
| 145 and 142 | 20590 |
| 110 and 73 | 8030 |
| 116 and 30 | 1740 |
| 153 and 157 | 24021 |