Least Common Multiple (LCM) of 110 and 71
The least common multiple (LCM) of 110 and 71 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 110 and 71?
First, calculate the GCD of 110 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 71 = 1 remainder 39 |
| 2 | 71 ÷ 39 = 1 remainder 32 |
| 3 | 39 ÷ 32 = 1 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 47 | 5405 |
| 161 and 54 | 8694 |
| 68 and 96 | 1632 |
| 47 and 114 | 5358 |
| 62 and 182 | 5642 |