Least Common Multiple (LCM) of 65 and 151
The least common multiple (LCM) of 65 and 151 is 9815.
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 151?
First, calculate the GCD of 65 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 151 = 0 remainder 65 |
| 2 | 151 ÷ 65 = 2 remainder 21 |
| 3 | 65 ÷ 21 = 3 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 45 | 495 |
| 46 and 175 | 8050 |
| 37 and 52 | 1924 |
| 105 and 21 | 105 |
| 53 and 103 | 5459 |