Least Common Multiple (LCM) of 53 and 89
The least common multiple (LCM) of 53 and 89 is 4717.
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 53 and 89?
First, calculate the GCD of 53 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 89 = 0 remainder 53 |
| 2 | 89 ÷ 53 = 1 remainder 36 |
| 3 | 53 ÷ 36 = 1 remainder 17 |
| 4 | 36 ÷ 17 = 2 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 128 | 14976 |
| 187 and 157 | 29359 |
| 135 and 170 | 4590 |
| 82 and 12 | 492 |
| 175 and 77 | 1925 |