Least Common Multiple (LCM) of 30 and 71
The least common multiple (LCM) of 30 and 71 is 2130.
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 30 and 71?
First, calculate the GCD of 30 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 71 = 0 remainder 30 |
| 2 | 71 ÷ 30 = 2 remainder 11 |
| 3 | 30 ÷ 11 = 2 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 155 | 16740 |
| 14 and 19 | 266 |
| 128 and 100 | 3200 |
| 34 and 71 | 2414 |
| 145 and 152 | 22040 |