Least Common Multiple (LCM) of 43 and 167
The least common multiple (LCM) of 43 and 167 is 7181.
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 43 and 167?
First, calculate the GCD of 43 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 167 = 0 remainder 43 |
| 2 | 167 ÷ 43 = 3 remainder 38 |
| 3 | 43 ÷ 38 = 1 remainder 5 |
| 4 | 38 ÷ 5 = 7 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 175 | 2100 |
| 104 and 72 | 936 |
| 14 and 60 | 420 |
| 185 and 153 | 28305 |
| 51 and 157 | 8007 |