Least Common Multiple (LCM) of 97 and 167
The least common multiple (LCM) of 97 and 167 is 16199.
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 167?
First, calculate the GCD of 97 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 167 = 0 remainder 97 |
| 2 | 167 ÷ 97 = 1 remainder 70 |
| 3 | 97 ÷ 70 = 1 remainder 27 |
| 4 | 70 ÷ 27 = 2 remainder 16 |
| 5 | 27 ÷ 16 = 1 remainder 11 |
| 6 | 16 ÷ 11 = 1 remainder 5 |
| 7 | 11 ÷ 5 = 2 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 37 | 1665 |
| 168 and 94 | 7896 |
| 16 and 199 | 3184 |
| 80 and 38 | 1520 |
| 132 and 34 | 2244 |