Least Common Multiple (LCM) of 65 and 22
The least common multiple (LCM) of 65 and 22 is 1430.
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 22?
First, calculate the GCD of 65 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 22 = 2 remainder 21 |
| 2 | 22 ÷ 21 = 1 remainder 1 |
| 3 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 143 | 15158 |
| 105 and 37 | 3885 |
| 200 and 168 | 4200 |
| 82 and 14 | 574 |
| 47 and 53 | 2491 |