Least Common Multiple (LCM) of 101 and 107
The least common multiple (LCM) of 101 and 107 is 10807.
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 101 and 107?
First, calculate the GCD of 101 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 107 = 0 remainder 101 |
| 2 | 107 ÷ 101 = 1 remainder 6 |
| 3 | 101 ÷ 6 = 16 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 17 | 340 |
| 11 and 183 | 2013 |
| 189 and 50 | 9450 |
| 66 and 178 | 5874 |
| 175 and 150 | 1050 |