Least Common Multiple (LCM) of 167 and 102
The least common multiple (LCM) of 167 and 102 is 17034.
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 102?
First, calculate the GCD of 167 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 102 = 1 remainder 65 |
| 2 | 102 ÷ 65 = 1 remainder 37 |
| 3 | 65 ÷ 37 = 1 remainder 28 |
| 4 | 37 ÷ 28 = 1 remainder 9 |
| 5 | 28 ÷ 9 = 3 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 41 | 123 |
| 81 and 38 | 3078 |
| 175 and 20 | 700 |
| 99 and 196 | 19404 |
| 129 and 162 | 6966 |