Least Common Multiple (LCM) of 74 and 191
The least common multiple (LCM) of 74 and 191 is 14134.
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 191?
First, calculate the GCD of 74 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 191 = 0 remainder 74 |
| 2 | 191 ÷ 74 = 2 remainder 43 |
| 3 | 74 ÷ 43 = 1 remainder 31 |
| 4 | 43 ÷ 31 = 1 remainder 12 |
| 5 | 31 ÷ 12 = 2 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 180 | 1260 |
| 33 and 137 | 4521 |
| 110 and 14 | 770 |
| 20 and 172 | 860 |
| 20 and 123 | 2460 |