Least Common Multiple (LCM) of 89 and 168
The least common multiple (LCM) of 89 and 168 is 14952.
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 89 and 168?
First, calculate the GCD of 89 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 168 = 0 remainder 89 |
| 2 | 168 ÷ 89 = 1 remainder 79 |
| 3 | 89 ÷ 79 = 1 remainder 10 |
| 4 | 79 ÷ 10 = 7 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 100 | 4300 |
| 147 and 178 | 26166 |
| 166 and 192 | 15936 |
| 107 and 43 | 4601 |
| 84 and 155 | 13020 |