Least Common Multiple (LCM) of 65 and 21
The least common multiple (LCM) of 65 and 21 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 65 and 21?
First, calculate the GCD of 65 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 21 = 3 remainder 2 |
| 2 | 21 ÷ 2 = 10 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 115 | 115 |
| 162 and 181 | 29322 |
| 195 and 157 | 30615 |
| 140 and 117 | 16380 |
| 142 and 158 | 11218 |