Least Common Multiple (LCM) of 105 and 69
The least common multiple (LCM) of 105 and 69 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 105 and 69?
First, calculate the GCD of 105 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 69 = 1 remainder 36 |
| 2 | 69 ÷ 36 = 1 remainder 33 |
| 3 | 36 ÷ 33 = 1 remainder 3 |
| 4 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 74 | 7178 |
| 101 and 53 | 5353 |
| 150 and 166 | 12450 |
| 126 and 194 | 12222 |
| 20 and 133 | 2660 |