Least Common Multiple (LCM) of 65 and 138
The least common multiple (LCM) of 65 and 138 is 8970.
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 138?
First, calculate the GCD of 65 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 138 = 0 remainder 65 |
| 2 | 138 ÷ 65 = 2 remainder 8 |
| 3 | 65 ÷ 8 = 8 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 145 | 16965 |
| 10 and 14 | 70 |
| 182 and 141 | 25662 |
| 16 and 37 | 592 |
| 45 and 109 | 4905 |