Least Common Multiple (LCM) of 22 and 65
The least common multiple (LCM) of 22 and 65 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 22 and 65?
First, calculate the GCD of 22 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 65 = 0 remainder 22 |
| 2 | 65 ÷ 22 = 2 remainder 21 |
| 3 | 22 ÷ 21 = 1 remainder 1 |
| 4 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 112 | 1120 |
| 169 and 51 | 8619 |
| 94 and 17 | 1598 |
| 31 and 10 | 310 |
| 112 and 77 | 1232 |