Least Common Multiple (LCM) of 71 and 117
The least common multiple (LCM) of 71 and 117 is 8307.
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 117?
First, calculate the GCD of 71 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 117 = 0 remainder 71 |
| 2 | 117 ÷ 71 = 1 remainder 46 |
| 3 | 71 ÷ 46 = 1 remainder 25 |
| 4 | 46 ÷ 25 = 1 remainder 21 |
| 5 | 25 ÷ 21 = 1 remainder 4 |
| 6 | 21 ÷ 4 = 5 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 32 | 672 |
| 134 and 25 | 3350 |
| 186 and 18 | 558 |
| 47 and 161 | 7567 |
| 16 and 112 | 112 |