Least Common Multiple (LCM) of 117 and 71
The least common multiple (LCM) of 117 and 71 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 117 and 71?
First, calculate the GCD of 117 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 71 = 1 remainder 46 |
| 2 | 71 ÷ 46 = 1 remainder 25 |
| 3 | 46 ÷ 25 = 1 remainder 21 |
| 4 | 25 ÷ 21 = 1 remainder 4 |
| 5 | 21 ÷ 4 = 5 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 67 | 10050 |
| 199 and 110 | 21890 |
| 143 and 169 | 1859 |
| 123 and 189 | 7749 |
| 133 and 168 | 3192 |