Least Common Multiple (LCM) of 167 and 190
The least common multiple (LCM) of 167 and 190 is 31730.
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 190?
First, calculate the GCD of 167 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 190 = 0 remainder 167 |
| 2 | 190 ÷ 167 = 1 remainder 23 |
| 3 | 167 ÷ 23 = 7 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 25 | 1825 |
| 106 and 32 | 1696 |
| 119 and 135 | 16065 |
| 200 and 174 | 17400 |
| 107 and 142 | 15194 |