Least Common Multiple (LCM) of 107 and 97
The least common multiple (LCM) of 107 and 97 is 10379.
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 97?
First, calculate the GCD of 107 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 97 = 1 remainder 10 |
| 2 | 97 ÷ 10 = 9 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 14 | 868 |
| 148 and 190 | 14060 |
| 199 and 100 | 19900 |
| 169 and 11 | 1859 |
| 79 and 124 | 9796 |