Least Common Multiple (LCM) of 69 and 110
The least common multiple (LCM) of 69 and 110 is 7590.
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 110?
First, calculate the GCD of 69 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 110 = 0 remainder 69 |
| 2 | 110 ÷ 69 = 1 remainder 41 |
| 3 | 69 ÷ 41 = 1 remainder 28 |
| 4 | 41 ÷ 28 = 1 remainder 13 |
| 5 | 28 ÷ 13 = 2 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 10 | 230 |
| 143 and 65 | 715 |
| 144 and 64 | 576 |
| 135 and 194 | 26190 |
| 105 and 19 | 1995 |