Least Common Multiple (LCM) of 46 and 71
The least common multiple (LCM) of 46 and 71 is 3266.
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 46 and 71?
First, calculate the GCD of 46 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 71 = 0 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 |
|---|---|
| 72 and 129 | 3096 |
| 160 and 107 | 17120 |
| 177 and 20 | 3540 |
| 162 and 155 | 25110 |
| 101 and 81 | 8181 |