Least Common Multiple (LCM) of 74 and 65
The least common multiple (LCM) of 74 and 65 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 74 and 65?
First, calculate the GCD of 74 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 65 = 1 remainder 9 |
| 2 | 65 ÷ 9 = 7 remainder 2 |
| 3 | 9 ÷ 2 = 4 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 55 | 5665 |
| 111 and 138 | 5106 |
| 119 and 191 | 22729 |
| 72 and 110 | 3960 |
| 153 and 29 | 4437 |