Least Common Multiple (LCM) of 65 and 78
The least common multiple (LCM) of 65 and 78 is 390.
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 78?
First, calculate the GCD of 65 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 78 = 0 remainder 65 |
| 2 | 78 ÷ 65 = 1 remainder 13 |
| 3 | 65 ÷ 13 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 131 | 1441 |
| 161 and 103 | 16583 |
| 98 and 113 | 11074 |
| 145 and 157 | 22765 |
| 125 and 115 | 2875 |