Least Common Multiple (LCM) of 167 and 107
The least common multiple (LCM) of 167 and 107 is 17869.
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 107?
First, calculate the GCD of 167 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 107 = 1 remainder 60 |
| 2 | 107 ÷ 60 = 1 remainder 47 |
| 3 | 60 ÷ 47 = 1 remainder 13 |
| 4 | 47 ÷ 13 = 3 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 151 | 16157 |
| 114 and 22 | 1254 |
| 79 and 71 | 5609 |
| 12 and 133 | 1596 |
| 19 and 14 | 266 |