Least Common Multiple (LCM) of 54 and 65
The least common multiple (LCM) of 54 and 65 is 3510.
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 65?
First, calculate the GCD of 54 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 65 = 0 remainder 54 |
| 2 | 65 ÷ 54 = 1 remainder 11 |
| 3 | 54 ÷ 11 = 4 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 121 | 13794 |
| 143 and 21 | 3003 |
| 137 and 112 | 15344 |
| 45 and 182 | 8190 |
| 147 and 123 | 6027 |