Least Common Multiple (LCM) of 65 and 139
The least common multiple (LCM) of 65 and 139 is 9035.
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 139?
First, calculate the GCD of 65 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 139 = 0 remainder 65 |
| 2 | 139 ÷ 65 = 2 remainder 9 |
| 3 | 65 ÷ 9 = 7 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 67 | 134 |
| 108 and 102 | 1836 |
| 33 and 80 | 2640 |
| 190 and 102 | 9690 |
| 130 and 121 | 15730 |