Least Common Multiple (LCM) of 74 and 107
The least common multiple (LCM) of 74 and 107 is 7918.
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 107?
First, calculate the GCD of 74 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 107 = 0 remainder 74 |
| 2 | 107 ÷ 74 = 1 remainder 33 |
| 3 | 74 ÷ 33 = 2 remainder 8 |
| 4 | 33 ÷ 8 = 4 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 144 | 7056 |
| 108 and 42 | 756 |
| 46 and 78 | 1794 |
| 17 and 66 | 1122 |
| 55 and 14 | 770 |