Least Common Multiple (LCM) of 110 and 69
The least common multiple (LCM) of 110 and 69 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 110 and 69?
First, calculate the GCD of 110 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 69 = 1 remainder 41 |
| 2 | 69 ÷ 41 = 1 remainder 28 |
| 3 | 41 ÷ 28 = 1 remainder 13 |
| 4 | 28 ÷ 13 = 2 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 39 | 6942 |
| 39 and 93 | 1209 |
| 130 and 160 | 2080 |
| 124 and 178 | 11036 |
| 123 and 185 | 22755 |