Least Common Multiple (LCM) of 71 and 90
The least common multiple (LCM) of 71 and 90 is 6390.
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 90?
First, calculate the GCD of 71 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 90 = 0 remainder 71 |
| 2 | 90 ÷ 71 = 1 remainder 19 |
| 3 | 71 ÷ 19 = 3 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 37 | 5883 |
| 138 and 193 | 26634 |
| 68 and 60 | 1020 |
| 65 and 116 | 7540 |
| 126 and 100 | 6300 |