Least Common Multiple (LCM) of 42 and 103
The least common multiple (LCM) of 42 and 103 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 42 and 103?
First, calculate the GCD of 42 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 103 = 0 remainder 42 |
| 2 | 103 ÷ 42 = 2 remainder 19 |
| 3 | 42 ÷ 19 = 2 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 163 | 16626 |
| 37 and 109 | 4033 |
| 15 and 184 | 2760 |
| 18 and 83 | 1494 |
| 76 and 46 | 1748 |