Least Common Multiple (LCM) of 117 and 97
The least common multiple (LCM) of 117 and 97 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 117 and 97?
First, calculate the GCD of 117 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 97 = 1 remainder 20 |
| 2 | 97 ÷ 20 = 4 remainder 17 |
| 3 | 20 ÷ 17 = 1 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 157 | 25277 |
| 196 and 125 | 24500 |
| 45 and 118 | 5310 |
| 190 and 99 | 18810 |
| 129 and 70 | 9030 |