Least Common Multiple (LCM) of 103 and 135
The least common multiple (LCM) of 103 and 135 is 13905.
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 135?
First, calculate the GCD of 103 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 135 = 0 remainder 103 |
| 2 | 135 ÷ 103 = 1 remainder 32 |
| 3 | 103 ÷ 32 = 3 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 94 | 5170 |
| 183 and 123 | 7503 |
| 72 and 34 | 1224 |
| 100 and 112 | 2800 |
| 140 and 60 | 420 |