Least Common Multiple (LCM) of 168 and 97
The least common multiple (LCM) of 168 and 97 is 16296.
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 168 and 97?
First, calculate the GCD of 168 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 97 = 1 remainder 71 |
| 2 | 97 ÷ 71 = 1 remainder 26 |
| 3 | 71 ÷ 26 = 2 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 108 | 864 |
| 190 and 113 | 21470 |
| 157 and 85 | 13345 |
| 68 and 129 | 8772 |
| 87 and 142 | 12354 |