Least Common Multiple (LCM) of 103 and 42
The least common multiple (LCM) of 103 and 42 is 4326.
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 42?
First, calculate the GCD of 103 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 42 = 2 remainder 19 |
| 2 | 42 ÷ 19 = 2 remainder 4 |
| 3 | 19 ÷ 4 = 4 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 38 | 38 |
| 71 and 62 | 4402 |
| 141 and 145 | 20445 |
| 186 and 41 | 7626 |
| 37 and 170 | 6290 |