Least Common Multiple (LCM) of 65 and 54
The least common multiple (LCM) of 65 and 54 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 65 and 54?
First, calculate the GCD of 65 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 54 = 1 remainder 11 |
| 2 | 54 ÷ 11 = 4 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 70 | 2240 |
| 135 and 110 | 2970 |
| 150 and 153 | 7650 |
| 187 and 145 | 27115 |
| 65 and 50 | 650 |