Least Common Multiple (LCM) of 103 and 134
The least common multiple (LCM) of 103 and 134 is 13802.
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 134?
First, calculate the GCD of 103 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 134 = 0 remainder 103 |
| 2 | 134 ÷ 103 = 1 remainder 31 |
| 3 | 103 ÷ 31 = 3 remainder 10 |
| 4 | 31 ÷ 10 = 3 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 61 | 8174 |
| 70 and 65 | 910 |
| 138 and 169 | 23322 |
| 185 and 28 | 5180 |
| 36 and 23 | 828 |