Least Common Multiple (LCM) of 65 and 74
The least common multiple (LCM) of 65 and 74 is 4810.
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 74?
First, calculate the GCD of 65 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 74 = 0 remainder 65 |
| 2 | 74 ÷ 65 = 1 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 |
|---|---|
| 38 and 171 | 342 |
| 102 and 138 | 2346 |
| 109 and 81 | 8829 |
| 11 and 194 | 2134 |
| 169 and 127 | 21463 |