Least Common Multiple (LCM) of 53 and 86
The least common multiple (LCM) of 53 and 86 is 4558.
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 86?
First, calculate the GCD of 53 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 86 = 0 remainder 53 |
| 2 | 86 ÷ 53 = 1 remainder 33 |
| 3 | 53 ÷ 33 = 1 remainder 20 |
| 4 | 33 ÷ 20 = 1 remainder 13 |
| 5 | 20 ÷ 13 = 1 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 114 | 4218 |
| 154 and 20 | 1540 |
| 67 and 165 | 11055 |
| 151 and 70 | 10570 |
| 76 and 139 | 10564 |