Least Common Multiple (LCM) of 21 and 65
The least common multiple (LCM) of 21 and 65 is 1365.
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 21 and 65?
First, calculate the GCD of 21 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 65 = 0 remainder 21 |
| 2 | 65 ÷ 21 = 3 remainder 2 |
| 3 | 21 ÷ 2 = 10 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 137 | 18495 |
| 182 and 54 | 4914 |
| 189 and 53 | 10017 |
| 16 and 130 | 1040 |
| 160 and 45 | 1440 |