Least Common Multiple (LCM) of 49 and 89
The least common multiple (LCM) of 49 and 89 is 4361.
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 49 and 89?
First, calculate the GCD of 49 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 89 = 0 remainder 49 |
| 2 | 89 ÷ 49 = 1 remainder 40 |
| 3 | 49 ÷ 40 = 1 remainder 9 |
| 4 | 40 ÷ 9 = 4 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 117 | 2106 |
| 136 and 39 | 5304 |
| 120 and 89 | 10680 |
| 90 and 125 | 2250 |
| 29 and 12 | 348 |