Least Common Multiple (LCM) of 168 and 43
The least common multiple (LCM) of 168 and 43 is 7224.
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 168 and 43?
First, calculate the GCD of 168 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 43 = 3 remainder 39 |
| 2 | 43 ÷ 39 = 1 remainder 4 |
| 3 | 39 ÷ 4 = 9 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 108 | 10476 |
| 44 and 78 | 1716 |
| 44 and 54 | 1188 |
| 117 and 153 | 1989 |
| 22 and 180 | 1980 |