Least Common Multiple (LCM) of 97 and 116
The least common multiple (LCM) of 97 and 116 is 11252.
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 116?
First, calculate the GCD of 97 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 116 = 0 remainder 97 |
| 2 | 116 ÷ 97 = 1 remainder 19 |
| 3 | 97 ÷ 19 = 5 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 107 | 1498 |
| 112 and 176 | 1232 |
| 65 and 161 | 10465 |
| 66 and 59 | 3894 |
| 70 and 172 | 6020 |