Least Common Multiple (LCM) of 74 and 121
The least common multiple (LCM) of 74 and 121 is 8954.
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 121?
First, calculate the GCD of 74 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 121 = 0 remainder 74 |
| 2 | 121 ÷ 74 = 1 remainder 47 |
| 3 | 74 ÷ 47 = 1 remainder 27 |
| 4 | 47 ÷ 27 = 1 remainder 20 |
| 5 | 27 ÷ 20 = 1 remainder 7 |
| 6 | 20 ÷ 7 = 2 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 22 | 2310 |
| 14 and 128 | 896 |
| 125 and 80 | 2000 |
| 189 and 63 | 189 |
| 44 and 191 | 8404 |