Least Common Multiple (LCM) of 71 and 67
The least common multiple (LCM) of 71 and 67 is 4757.
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 67?
First, calculate the GCD of 71 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 67 = 1 remainder 4 |
| 2 | 67 ÷ 4 = 16 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 159 | 17967 |
| 198 and 172 | 17028 |
| 128 and 114 | 7296 |
| 155 and 174 | 26970 |
| 142 and 28 | 1988 |