Least Common Multiple (LCM) of 107 and 71
The least common multiple (LCM) of 107 and 71 is 7597.
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 107 and 71?
First, calculate the GCD of 107 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 71 = 1 remainder 36 |
| 2 | 71 ÷ 36 = 1 remainder 35 |
| 3 | 36 ÷ 35 = 1 remainder 1 |
| 4 | 35 ÷ 1 = 35 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 50 | 800 |
| 100 and 172 | 4300 |
| 19 and 162 | 3078 |
| 12 and 45 | 180 |
| 111 and 112 | 12432 |