Least Common Multiple (LCM) of 15 and 71
The least common multiple (LCM) of 15 and 71 is 1065.
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 15 and 71?
First, calculate the GCD of 15 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 71 = 0 remainder 15 |
| 2 | 71 ÷ 15 = 4 remainder 11 |
| 3 | 15 ÷ 11 = 1 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 130 | 8710 |
| 53 and 16 | 848 |
| 116 and 157 | 18212 |
| 173 and 197 | 34081 |
| 83 and 142 | 11786 |