Least Common Multiple (LCM) of 42 and 89
The least common multiple (LCM) of 42 and 89 is 3738.
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 42 and 89?
First, calculate the GCD of 42 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 89 = 0 remainder 42 |
| 2 | 89 ÷ 42 = 2 remainder 5 |
| 3 | 42 ÷ 5 = 8 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 144 | 15696 |
| 66 and 93 | 2046 |
| 77 and 99 | 693 |
| 104 and 122 | 6344 |
| 174 and 137 | 23838 |