Least Common Multiple (LCM) of 102 and 167
The least common multiple (LCM) of 102 and 167 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 102 and 167?
First, calculate the GCD of 102 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 167 = 0 remainder 102 |
| 2 | 167 ÷ 102 = 1 remainder 65 |
| 3 | 102 ÷ 65 = 1 remainder 37 |
| 4 | 65 ÷ 37 = 1 remainder 28 |
| 5 | 37 ÷ 28 = 1 remainder 9 |
| 6 | 28 ÷ 9 = 3 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 112 | 224 |
| 188 and 127 | 23876 |
| 108 and 162 | 324 |
| 165 and 116 | 19140 |
| 93 and 111 | 3441 |