Least Common Multiple (LCM) of 53 and 87
The least common multiple (LCM) of 53 and 87 is 4611.
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 87?
First, calculate the GCD of 53 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 87 = 0 remainder 53 |
| 2 | 87 ÷ 53 = 1 remainder 34 |
| 3 | 53 ÷ 34 = 1 remainder 19 |
| 4 | 34 ÷ 19 = 1 remainder 15 |
| 5 | 19 ÷ 15 = 1 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 90 | 16290 |
| 15 and 178 | 2670 |
| 122 and 133 | 16226 |
| 16 and 165 | 2640 |
| 78 and 133 | 10374 |