Least Common Multiple (LCM) of 114 and 71
The least common multiple (LCM) of 114 and 71 is 8094.
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 114 and 71?
First, calculate the GCD of 114 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 71 = 1 remainder 43 |
| 2 | 71 ÷ 43 = 1 remainder 28 |
| 3 | 43 ÷ 28 = 1 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 138 | 3450 |
| 134 and 174 | 11658 |
| 110 and 140 | 1540 |
| 12 and 175 | 2100 |
| 17 and 70 | 1190 |