Least Common Multiple (LCM) of 97 and 114
The least common multiple (LCM) of 97 and 114 is 11058.
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 114?
First, calculate the GCD of 97 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 114 = 0 remainder 97 |
| 2 | 114 ÷ 97 = 1 remainder 17 |
| 3 | 97 ÷ 17 = 5 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 14 | 112 |
| 158 and 64 | 5056 |
| 138 and 120 | 2760 |
| 62 and 192 | 5952 |
| 185 and 45 | 1665 |