Least Common Multiple (LCM) of 14 and 65
The least common multiple (LCM) of 14 and 65 is 910.
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 14 and 65?
First, calculate the GCD of 14 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 65 = 0 remainder 14 |
| 2 | 65 ÷ 14 = 4 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 139 | 4309 |
| 99 and 14 | 1386 |
| 48 and 120 | 240 |
| 106 and 50 | 2650 |
| 119 and 33 | 3927 |