Least Common Multiple (LCM) of 108 and 97
The least common multiple (LCM) of 108 and 97 is 10476.
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 108 and 97?
First, calculate the GCD of 108 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 97 = 1 remainder 11 |
| 2 | 97 ÷ 11 = 8 remainder 9 |
| 3 | 11 ÷ 9 = 1 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 96 | 18528 |
| 179 and 104 | 18616 |
| 62 and 194 | 6014 |
| 116 and 110 | 6380 |
| 81 and 169 | 13689 |