Least Common Multiple (LCM) of 69 and 111
The least common multiple (LCM) of 69 and 111 is 2553.
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 111?
First, calculate the GCD of 69 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 111 = 0 remainder 69 |
| 2 | 111 ÷ 69 = 1 remainder 42 |
| 3 | 69 ÷ 42 = 1 remainder 27 |
| 4 | 42 ÷ 27 = 1 remainder 15 |
| 5 | 27 ÷ 15 = 1 remainder 12 |
| 6 | 15 ÷ 12 = 1 remainder 3 |
| 7 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 62 | 8494 |
| 52 and 23 | 1196 |
| 10 and 83 | 830 |
| 45 and 99 | 495 |
| 159 and 179 | 28461 |