Least Common Multiple (LCM) of 167 and 116
The least common multiple (LCM) of 167 and 116 is 19372.
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 116?
First, calculate the GCD of 167 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 116 = 1 remainder 51 |
| 2 | 116 ÷ 51 = 2 remainder 14 |
| 3 | 51 ÷ 14 = 3 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 85 | 13345 |
| 159 and 189 | 10017 |
| 190 and 114 | 570 |
| 195 and 108 | 7020 |
| 76 and 85 | 6460 |