Least Common Multiple (LCM) of 29 and 99
The least common multiple (LCM) of 29 and 99 is 2871.
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 99?
First, calculate the GCD of 29 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 99 = 0 remainder 29 |
| 2 | 99 ÷ 29 = 3 remainder 12 |
| 3 | 29 ÷ 12 = 2 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 149 | 25330 |
| 53 and 10 | 530 |
| 39 and 185 | 7215 |
| 123 and 22 | 2706 |
| 130 and 34 | 2210 |