Least Common Multiple (LCM) of 71 and 110
The least common multiple (LCM) of 71 and 110 is 7810.
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 71 and 110?
First, calculate the GCD of 71 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 110 = 0 remainder 71 |
| 2 | 110 ÷ 71 = 1 remainder 39 |
| 3 | 71 ÷ 39 = 1 remainder 32 |
| 4 | 39 ÷ 32 = 1 remainder 7 |
| 5 | 32 ÷ 7 = 4 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 65 | 3705 |
| 126 and 161 | 2898 |
| 142 and 144 | 10224 |
| 153 and 180 | 3060 |
| 65 and 42 | 2730 |