Least Common Multiple (LCM) of 120 and 71
The least common multiple (LCM) of 120 and 71 is 8520.
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 120 and 71?
First, calculate the GCD of 120 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 71 = 1 remainder 49 |
| 2 | 71 ÷ 49 = 1 remainder 22 |
| 3 | 49 ÷ 22 = 2 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 171 | 7011 |
| 105 and 119 | 1785 |
| 162 and 99 | 1782 |
| 59 and 116 | 6844 |
| 60 and 50 | 300 |