Least Common Multiple (LCM) of 54 and 87
The least common multiple (LCM) of 54 and 87 is 1566.
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 54 and 87?
First, calculate the GCD of 54 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 87 = 0 remainder 54 |
| 2 | 87 ÷ 54 = 1 remainder 33 |
| 3 | 54 ÷ 33 = 1 remainder 21 |
| 4 | 33 ÷ 21 = 1 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 62 | 3038 |
| 192 and 165 | 10560 |
| 83 and 34 | 2822 |
| 52 and 17 | 884 |
| 177 and 22 | 3894 |