Least Common Multiple (LCM) of 69 and 99
The least common multiple (LCM) of 69 and 99 is 2277.
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 69 and 99?
First, calculate the GCD of 69 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 99 = 0 remainder 69 |
| 2 | 99 ÷ 69 = 1 remainder 30 |
| 3 | 69 ÷ 30 = 2 remainder 9 |
| 4 | 30 ÷ 9 = 3 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 67 | 3417 |
| 120 and 185 | 4440 |
| 90 and 26 | 1170 |
| 32 and 24 | 96 |
| 53 and 26 | 1378 |