Least Common Multiple (LCM) of 97 and 69
The least common multiple (LCM) of 97 and 69 is 6693.
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 69?
First, calculate the GCD of 97 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 69 = 1 remainder 28 |
| 2 | 69 ÷ 28 = 2 remainder 13 |
| 3 | 28 ÷ 13 = 2 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 114 | 4218 |
| 18 and 85 | 1530 |
| 134 and 105 | 14070 |
| 160 and 21 | 3360 |
| 165 and 190 | 6270 |