Least Common Multiple (LCM) of 135 and 103
The least common multiple (LCM) of 135 and 103 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 135 and 103?
First, calculate the GCD of 135 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 103 = 1 remainder 32 |
| 2 | 103 ÷ 32 = 3 remainder 7 |
| 3 | 32 ÷ 7 = 4 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 176 | 11088 |
| 176 and 84 | 3696 |
| 100 and 80 | 400 |
| 193 and 12 | 2316 |
| 138 and 16 | 1104 |