Least Common Multiple (LCM) of 97 and 108
The least common multiple (LCM) of 97 and 108 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 97 and 108?
First, calculate the GCD of 97 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 108 = 0 remainder 97 |
| 2 | 108 ÷ 97 = 1 remainder 11 |
| 3 | 97 ÷ 11 = 8 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 193 | 18914 |
| 27 and 192 | 1728 |
| 103 and 172 | 17716 |
| 120 and 76 | 2280 |
| 120 and 115 | 2760 |