Least Common Multiple (LCM) of 29 and 103
The least common multiple (LCM) of 29 and 103 is 2987.
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 29 and 103?
First, calculate the GCD of 29 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 103 = 0 remainder 29 |
| 2 | 103 ÷ 29 = 3 remainder 16 |
| 3 | 29 ÷ 16 = 1 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 183 | 6954 |
| 105 and 105 | 105 |
| 125 and 28 | 3500 |
| 106 and 29 | 3074 |
| 100 and 39 | 3900 |