Least Common Multiple (LCM) of 40 and 89
The least common multiple (LCM) of 40 and 89 is 3560.
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 40 and 89?
First, calculate the GCD of 40 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 89 = 0 remainder 40 |
| 2 | 89 ÷ 40 = 2 remainder 9 |
| 3 | 40 ÷ 9 = 4 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 108 | 18900 |
| 87 and 155 | 13485 |
| 195 and 95 | 3705 |
| 105 and 62 | 6510 |
| 15 and 112 | 1680 |