Least Common Multiple (LCM) of 29 and 97
The least common multiple (LCM) of 29 and 97 is 2813.
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 97?
First, calculate the GCD of 29 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 97 = 0 remainder 29 |
| 2 | 97 ÷ 29 = 3 remainder 10 |
| 3 | 29 ÷ 10 = 2 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 132 | 4620 |
| 85 and 69 | 5865 |
| 12 and 29 | 348 |
| 30 and 173 | 5190 |
| 68 and 89 | 6052 |