Least Common Multiple (LCM) of 106 and 69
The least common multiple (LCM) of 106 and 69 is 7314.
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 106 and 69?
First, calculate the GCD of 106 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 69 = 1 remainder 37 |
| 2 | 69 ÷ 37 = 1 remainder 32 |
| 3 | 37 ÷ 32 = 1 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 61 | 2989 |
| 97 and 58 | 5626 |
| 105 and 102 | 3570 |
| 45 and 85 | 765 |
| 151 and 168 | 25368 |