Least Common Multiple (LCM) of 69 and 109
The least common multiple (LCM) of 69 and 109 is 7521.
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 109?
First, calculate the GCD of 69 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 109 = 0 remainder 69 |
| 2 | 109 ÷ 69 = 1 remainder 40 |
| 3 | 69 ÷ 40 = 1 remainder 29 |
| 4 | 40 ÷ 29 = 1 remainder 11 |
| 5 | 29 ÷ 11 = 2 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 145 | 2030 |
| 138 and 106 | 7314 |
| 106 and 173 | 18338 |
| 112 and 159 | 17808 |
| 108 and 159 | 5724 |