Least Common Multiple (LCM) of 29 and 107
The least common multiple (LCM) of 29 and 107 is 3103.
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 107?
First, calculate the GCD of 29 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 107 = 0 remainder 29 |
| 2 | 107 ÷ 29 = 3 remainder 20 |
| 3 | 29 ÷ 20 = 1 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 180 | 1440 |
| 122 and 40 | 2440 |
| 179 and 80 | 14320 |
| 42 and 135 | 1890 |
| 194 and 98 | 9506 |