Least Common Multiple (LCM) of 167 and 97
The least common multiple (LCM) of 167 and 97 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 167 and 97?
First, calculate the GCD of 167 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 97 = 1 remainder 70 |
| 2 | 97 ÷ 70 = 1 remainder 27 |
| 3 | 70 ÷ 27 = 2 remainder 16 |
| 4 | 27 ÷ 16 = 1 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 101 | 8383 |
| 19 and 104 | 1976 |
| 188 and 13 | 2444 |
| 90 and 102 | 1530 |
| 94 and 142 | 6674 |