Least Common Multiple (LCM) of 65 and 91
The least common multiple (LCM) of 65 and 91 is 455.
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 91?
First, calculate the GCD of 65 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 91 = 0 remainder 65 |
| 2 | 91 ÷ 65 = 1 remainder 26 |
| 3 | 65 ÷ 26 = 2 remainder 13 |
| 4 | 26 ÷ 13 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 132 | 4620 |
| 18 and 53 | 954 |
| 93 and 107 | 9951 |
| 141 and 68 | 9588 |
| 36 and 124 | 1116 |