Least Common Multiple (LCM) of 107 and 110
The least common multiple (LCM) of 107 and 110 is 11770.
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 107 and 110?
First, calculate the GCD of 107 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 110 = 0 remainder 107 |
| 2 | 110 ÷ 107 = 1 remainder 3 |
| 3 | 107 ÷ 3 = 35 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 122 | 23058 |
| 153 and 177 | 9027 |
| 107 and 147 | 15729 |
| 53 and 143 | 7579 |
| 98 and 36 | 1764 |