Least Common Multiple (LCM) of 97 and 117
The least common multiple (LCM) of 97 and 117 is 11349.
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 117?
First, calculate the GCD of 97 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 117 = 0 remainder 97 |
| 2 | 117 ÷ 97 = 1 remainder 20 |
| 3 | 97 ÷ 20 = 4 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 79 | 11218 |
| 161 and 13 | 2093 |
| 149 and 65 | 9685 |
| 105 and 145 | 3045 |
| 86 and 84 | 3612 |