Least Common Multiple (LCM) of 74 and 106
The least common multiple (LCM) of 74 and 106 is 3922.
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 106?
First, calculate the GCD of 74 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 106 = 0 remainder 74 |
| 2 | 106 ÷ 74 = 1 remainder 32 |
| 3 | 74 ÷ 32 = 2 remainder 10 |
| 4 | 32 ÷ 10 = 3 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 65 | 1950 |
| 161 and 20 | 3220 |
| 33 and 97 | 3201 |
| 87 and 155 | 13485 |
| 132 and 199 | 26268 |