Least Common Multiple (LCM) of 107 and 91
The least common multiple (LCM) of 107 and 91 is 9737.
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 91?
First, calculate the GCD of 107 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 91 = 1 remainder 16 |
| 2 | 91 ÷ 16 = 5 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 33 | 462 |
| 63 and 109 | 6867 |
| 167 and 13 | 2171 |
| 117 and 48 | 1872 |
| 188 and 150 | 14100 |