Least Common Multiple (LCM) of 29 and 47
The least common multiple (LCM) of 29 and 47 is 1363.
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 47?
First, calculate the GCD of 29 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 47 = 0 remainder 29 |
| 2 | 47 ÷ 29 = 1 remainder 18 |
| 3 | 29 ÷ 18 = 1 remainder 11 |
| 4 | 18 ÷ 11 = 1 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 200 | 8200 |
| 105 and 116 | 12180 |
| 17 and 193 | 3281 |
| 149 and 197 | 29353 |
| 62 and 106 | 3286 |