Least Common Multiple (LCM) of 65 and 101
The least common multiple (LCM) of 65 and 101 is 6565.
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 101?
First, calculate the GCD of 65 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 101 = 0 remainder 65 |
| 2 | 101 ÷ 65 = 1 remainder 36 |
| 3 | 65 ÷ 36 = 1 remainder 29 |
| 4 | 36 ÷ 29 = 1 remainder 7 |
| 5 | 29 ÷ 7 = 4 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 55 | 2970 |
| 99 and 85 | 8415 |
| 102 and 150 | 2550 |
| 35 and 128 | 4480 |
| 116 and 153 | 17748 |