Least Common Multiple (LCM) of 105 and 74
The least common multiple (LCM) of 105 and 74 is 7770.
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 105 and 74?
First, calculate the GCD of 105 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 74 = 1 remainder 31 |
| 2 | 74 ÷ 31 = 2 remainder 12 |
| 3 | 31 ÷ 12 = 2 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 95 | 11305 |
| 117 and 128 | 14976 |
| 11 and 173 | 1903 |
| 69 and 162 | 3726 |
| 146 and 173 | 25258 |