Least Common Multiple (LCM) of 103 and 35
The least common multiple (LCM) of 103 and 35 is 3605.
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 35?
First, calculate the GCD of 103 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 35 = 2 remainder 33 |
| 2 | 35 ÷ 33 = 1 remainder 2 |
| 3 | 33 ÷ 2 = 16 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 38 | 1596 |
| 116 and 191 | 22156 |
| 88 and 93 | 8184 |
| 43 and 142 | 6106 |
| 126 and 54 | 378 |