Least Common Multiple (LCM) of 69 and 105
The least common multiple (LCM) of 69 and 105 is 2415.
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 105?
First, calculate the GCD of 69 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 105 = 0 remainder 69 |
| 2 | 105 ÷ 69 = 1 remainder 36 |
| 3 | 69 ÷ 36 = 1 remainder 33 |
| 4 | 36 ÷ 33 = 1 remainder 3 |
| 5 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 187 | 21131 |
| 180 and 131 | 23580 |
| 10 and 178 | 890 |
| 87 and 25 | 2175 |
| 63 and 173 | 10899 |