Least Common Multiple (LCM) of 89 and 142
The least common multiple (LCM) of 89 and 142 is 12638.
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 142?
First, calculate the GCD of 89 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 142 = 0 remainder 89 |
| 2 | 142 ÷ 89 = 1 remainder 53 |
| 3 | 89 ÷ 53 = 1 remainder 36 |
| 4 | 53 ÷ 36 = 1 remainder 17 |
| 5 | 36 ÷ 17 = 2 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 71 | 13064 |
| 20 and 114 | 1140 |
| 144 and 131 | 18864 |
| 116 and 48 | 1392 |
| 181 and 133 | 24073 |