Least Common Multiple (LCM) of 109 and 74
The least common multiple (LCM) of 109 and 74 is 8066.
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 109 and 74?
First, calculate the GCD of 109 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 74 = 1 remainder 35 |
| 2 | 74 ÷ 35 = 2 remainder 4 |
| 3 | 35 ÷ 4 = 8 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 46 | 2484 |
| 75 and 68 | 5100 |
| 56 and 100 | 1400 |
| 172 and 59 | 10148 |
| 134 and 104 | 6968 |